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The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone.

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Pre-Calculus 11 - Lesson no. 1: Conic Sections

This is a powerpoint presentation that discusses about the topic or lesson: Conic Sections. It also includes the definition, types and some terminologies involved in the topic: Conic Sections.

Conic section ppt

This document provides information about different conic sections including circles, parabolas, ellipses, and hyperbolas. It defines each conic section, gives their key properties and equations, and provides examples of how they appear in nature. The three conic sections that are created when a double cone is intersected with a plane are parabolas, circles and ellipses, and hyperbolas. Each type of conic section is defined by its focal properties and relationships.

Conic section Maths Class 11

The document discusses different conic sections including circles, parabolas, and their standard forms. A circle is defined as all points equidistant from a fixed center point. The standard form of a circle is (x-h)2 + (y-k)2 = r2, where (h,k) is the center and r is the radius. A parabola is defined as all points equidistant from a fixed focus point and directrix line. The standard forms of parabolas that open up, down, left or right are presented based on the location of the vertex, focus and directrix.

Conic sections and introduction to circles

Conic sections are shapes that result from slicing a cone with a plane. There are four types of conic sections: circles, ellipses, parabolas, and hyperbolas. Circles can be defined by the general formula x^2 + y^2 = r^2, where all points are a distance r from the center. The center and radius of a circle can be determined by shifting the circle and setting the x and y components to 0.

PRE-CALCULUS (Lesson 1-Conic Sections and Circles).pptx

This document discusses pre-calculus concepts related to conic sections including circles. It defines conic sections as curves formed by the intersection of a plane and a double right circular cone. The main types of conic sections are defined as circles, ellipses, parabolas, and hyperbolas. Circles are defined as sets of points equidistant from a fixed center point, and the standard form of a circle equation is given as (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius. Several examples are provided of writing the standard form of circle equations given the center and radius.

Conic Section

This document discusses the four basic conic sections - circles, parabolas, ellipses, and hyperbolas. It provides the standard form equations and key characteristics for each conic section with varying positions of the vertex. Circles are defined by a center point and radius. Parabolas are defined by a focus, directrix, and vertex. Ellipses are defined by two foci and the sum of distances to these points. Hyperbolas are defined by two foci and the difference of distances to these points. Examples of each conic section in architecture and acoustics are also given.

Conic Section

MS Report, When we talked about the conic section it involves a double-napped cone and a plane. If a plane intersects a double right circular cone, we get two-dimensional curves of different types. These curves are what we called the conic section.

Introduction to conic sections

The document discusses precalculus concepts related to conic sections including circles, ellipses, parabolas, and hyperbolas. It defines a circle as the set of all points that are the same distance from a given center point, and provides the standard form equation for a circle. Examples are given of writing the standard form equation for various circles described by their graphical representations, centers, radii, or tangency conditions.

Pre-Calculus 11 - Lesson no. 1: Conic Sections

This is a powerpoint presentation that discusses about the topic or lesson: Conic Sections. It also includes the definition, types and some terminologies involved in the topic: Conic Sections.

Conic section ppt

This document provides information about different conic sections including circles, parabolas, ellipses, and hyperbolas. It defines each conic section, gives their key properties and equations, and provides examples of how they appear in nature. The three conic sections that are created when a double cone is intersected with a plane are parabolas, circles and ellipses, and hyperbolas. Each type of conic section is defined by its focal properties and relationships.

Conic section Maths Class 11

The document discusses different conic sections including circles, parabolas, and their standard forms. A circle is defined as all points equidistant from a fixed center point. The standard form of a circle is (x-h)2 + (y-k)2 = r2, where (h,k) is the center and r is the radius. A parabola is defined as all points equidistant from a fixed focus point and directrix line. The standard forms of parabolas that open up, down, left or right are presented based on the location of the vertex, focus and directrix.

Conic sections and introduction to circles

Conic sections are shapes that result from slicing a cone with a plane. There are four types of conic sections: circles, ellipses, parabolas, and hyperbolas. Circles can be defined by the general formula x^2 + y^2 = r^2, where all points are a distance r from the center. The center and radius of a circle can be determined by shifting the circle and setting the x and y components to 0.

PRE-CALCULUS (Lesson 1-Conic Sections and Circles).pptx

This document discusses pre-calculus concepts related to conic sections including circles. It defines conic sections as curves formed by the intersection of a plane and a double right circular cone. The main types of conic sections are defined as circles, ellipses, parabolas, and hyperbolas. Circles are defined as sets of points equidistant from a fixed center point, and the standard form of a circle equation is given as (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius. Several examples are provided of writing the standard form of circle equations given the center and radius.

Conic Section

This document discusses the four basic conic sections - circles, parabolas, ellipses, and hyperbolas. It provides the standard form equations and key characteristics for each conic section with varying positions of the vertex. Circles are defined by a center point and radius. Parabolas are defined by a focus, directrix, and vertex. Ellipses are defined by two foci and the sum of distances to these points. Hyperbolas are defined by two foci and the difference of distances to these points. Examples of each conic section in architecture and acoustics are also given.

Conic Section

MS Report, When we talked about the conic section it involves a double-napped cone and a plane. If a plane intersects a double right circular cone, we get two-dimensional curves of different types. These curves are what we called the conic section.

Introduction to conic sections

The document discusses precalculus concepts related to conic sections including circles, ellipses, parabolas, and hyperbolas. It defines a circle as the set of all points that are the same distance from a given center point, and provides the standard form equation for a circle. Examples are given of writing the standard form equation for various circles described by their graphical representations, centers, radii, or tangency conditions.

Lesson 9 conic sections - ellipse

An ellipse is defined as the set of all points where the sum of the distances from two fixed points (foci) is a constant (the length of the major axis). Key properties include:
- The vertices are the endpoints of the major axis.
- The distance from the center to each focus is the eccentricity.
- The general equation of an ellipse with center at (h,k) is (x-h)^2/a^2 + (y-k)^2/b^2 = 1.
- Examples are provided to illustrate finding the equation of an ellipse given properties like the foci, vertices, or axes.

Conic sectioins

This document defines and provides the standard forms of conic sections, including circles, ellipses, parabolas, and hyperbolas. It explains that a circle is a closed loop where each point is a fixed distance from the center. A parabola is the set of points equidistant from a directrix and focus. An ellipse is the set of points where the sum of distances to two foci is constant. A hyperbola is the set of points where the difference between distances to two foci is constant. Standard forms are provided for each conic section with the vertex or center at (0,0) or (h,k) and characteristics like vertices and foci.

ellipse (An Introduction)

An ellipse is a curve where the sum of the distances from two fixed focal points is a constant. It is defined as the set of all points whose distances from two focal points add up to a constant. The standard equation of an ellipse is (x/a)^2 + (y/b)^2 = 1, where the focal points are located at (±c,0) and the vertices are located at (±a,0) and covertices at (0,±b). Examples are given of finding the focal points, vertices, and covertices of ellipses with given standard equations and of writing the standard equation of an ellipse given its focal points and constant sum of distances.

Conic Sections- Circle, Parabola, Ellipse, Hyperbola

Conic Sections- Circle, Parabola, Ellipse, Hyperbola all topics covered. this is a presentation with excelent animations and explatition.

Lesson 8 conic sections - parabola

The document defines conic sections and describes parabolas. It provides specific objectives related to defining conic sections, identifying different types, describing parabolas, and converting between general and standard forms of parabola equations. It then gives details on the focus, directrix, vertex, latus rectum, and eccentricity of parabolas. Examples of problems involving finding parabola equations and properties from conditions are also provided.

CONIC SECTIONS AND ITS APPLICATIONS

This document defines and provides examples of different types of conic sections - parabolas, ellipses, and hyperbolas. It explains that conic sections are curves formed by the intersection of a plane with a cone, and that points on a conic section have a fixed ratio between their distance to a focus point and its directrix line, known as eccentricity. Eccentricity values distinguish the different conic section types. Examples of each in diagrams and applications like planetary orbits, bicycle gears, and network synchronization are also provided.

Parabola

The document discusses parabolas and their key properties:
- A parabola is the set of all points equidistant from a fixed line called the directrix and a fixed point called the focus.
- The standard equation of a parabola depends on the orientation of its axis and vertex.
- Key properties include the axis of symmetry, direction of opening, and the length of the latus rectum.

Pre-Calculus: Conics - Introduction to Conics and Determining & Graphing Circ...

This PowerPoint contains an introduction to conical sections: the conics formed from double-napped circular cone - the Parabola, Hyperbola, Circle, & Ellipse. It also contains the basic parts of Circle. Identifying the standard form of circle's radius and center. Graphing a circle from its standard form. Transforming General Equation of Circle to Standard Form and some of the special cases.

Properties of circle

Some properties of tangents, secants and chords, Angles formed by intersecting chords, tangent and chord and two secants, Chords and their arcs, Segments of chords secants and tangents, Lengths of arcs and areas of sectors

Ellipse

An ellipse is a curve in a plane where the sum of the distances to two fixed points (foci) is a constant. The two foci, along with the major and minor axes and vertices, are used to define an ellipse. The standard equation of an ellipse depends on whether the foci lie along the x-axis or y-axis. Key properties including eccentricity and the latus rectum are also described.

Ellipse

An ellipse is defined algebraically as the set of all points where the sum of the distances to two fixed points (the foci) is a constant. Geometrically, an ellipse can be constructed by stretching a circle: using a piece of string fixed at both ends (the foci) and tracing the path of a pencil as it is moved around so that the total length of string remains constant.
The standard equation of an ellipse is (x-h)2/a2 + (y-k)2/b2 = 1, where (h,k) is the center and a and b are the lengths of the semi-major and semi-minor axes. To graph an ellipse, one plots

Equations of circles

This document discusses graphing circles and converting between graphing form and standard form equations of circles. It provides examples of writing the equation of a circle given its center and radius in graphing form. It also shows how to find the center, radius, and equation of a circle given the standard form equation. The key points are:
- In graphing form, the center is denoted as (h, k) and the equation is (x - h)2 + (y - k)2 = r2
- To convert to standard form, complete the square and factor the left side, moving any constant to the right side.

6.14.1 Arcs, Chords, and Angles

This document defines key terms and concepts related to circles, arcs, chords, and tangents. It defines circles, diameters, radii, central angles, secants, chords, tangents, and points of tangency. It presents theorems about perpendicular lines being tangent to a circle, congruent tangent segments, and radii/diameters bisecting chords and arcs. Examples demonstrate finding measures of arcs and angles, and calculating lengths based on circle properties.

Equation of Hyperbola

The document provides information about hyperbolas including:
- A hyperbola is defined as the set of all points where the difference between the distances to two fixed points (foci) is a constant.
- Key properties include two foci, a transverse axis connecting the foci, a conjugate axis perpendicular to the transverse axis, and vertices where it intersects the transverse axis.
- The standard equation of a hyperbola with foci on the x-axis is (y2/b2) - (x2/a2) = 1, where a and b are related to the distances between the foci and vertices.

parabola class 12

This document discusses parabolas, including their key features like the vertex, focus, directrix, and axis of symmetry. It provides examples of how to graph parabolas given their standard form equations, both for parabolas with vertices at the origin and for parabolas with other vertices. It also shows how to write the standard form equation of a parabola when given its focus and directrix.

Quadratic functions

The document discusses quadratic functions and their graphs. It defines quadratic functions as functions of the form f(x)=ax^2+bx+c, where a is not equal to 0. The graph of a quadratic function is a parabola with certain characteristics: it is symmetrical about an axis of symmetry and has a vertex which is either a maximum or minimum point. The axis of symmetry is the line x=0 for functions of the form f(x)=ax^2 and the vertex is at (0,0). For functions of the form f(x)=ax^2+k, the graph is a translation of f(x)=ax^2, so the vertex is (0,k) and the

Ellipse

This document discusses analytic geometry and ellipses. It begins with objectives of defining key terms of conic sections like ellipses, and solving equations and real-world problems involving ellipses. An activity is described where students can draw an ellipse using a rubber band stretched between two pins. Examples of completed ellipses are shown along with their equations and key properties labeled like foci, vertices, axes, and eccentricity. Students are given practice problems to find properties of ellipses based on given information.

Parabola

The document discusses parabolas and their key properties:
- A parabola is defined as the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
- The vertex is the point where the axis of symmetry intersects the parabola. The focus and directrix are a fixed distance (p) from the vertex.
- The latus rectum is the line segment from the focus to the parabola, perpendicular to the axis of symmetry. Its length is determined by the equation of the parabola.

class 10 circles

- A circle is the set of all points in a plane that are equidistant from a fixed point called the center.
- Important terms related to circles include chord, diameter, arc, sector, minor/major segments.
- A tangent touches the circle at one point, a secant intersects at two points, and there can be at most two parallel tangents for a given secant.
- The tangent radius theorem states that the tangent is perpendicular to the radius at the point of contact. The equal tangent lengths theorem says tangents from an external point are equal in length.

Conic sections

This document discusses conic sections, including circles, ellipses, parabolas, and hyperbolas. It provides:
1) The definitions and standard equations of each conic section, describing how they are formed from the intersection of a plane with a double cone.
2) Examples of different forms the equations can take and the geometric properties of each conic section, such as foci, axes, vertices, and asymptotes.
3) Methods for writing the equations of tangents to conics and using parametric equations to represent loci.
In less than 3 sentences, it summarizes the key information about conic sections provided in the document.

Paso 4_Álgebra, trigonometría y Geometría Analítica

The document discusses different types of conic sections including circles, ellipses, hyperbolas, and parabolas. It provides the general equation for conic sections and the conditions to determine which type of conic section is represented based on the values of certain coefficients in the equation. It then gives the standard forms of the equations for each type of conic section and discusses some of their defining geometric properties.

math conic sections.pptx

This document discusses parabolas as a type of conic section. It defines key properties of parabolas including the vertex, focal length, latus rectum, and directrix. The standard and vertex forms of the parabolic equation are presented. Methods for graphing parabolas by plotting points from an equation are described. An example problem calculates the depth of a satellite dish with a parabolic cross-section given its width and the distance to the focus. Real-world applications of parabolas in satellite dishes, heaters, and arched structures are briefly mentioned.

Lesson 9 conic sections - ellipse

An ellipse is defined as the set of all points where the sum of the distances from two fixed points (foci) is a constant (the length of the major axis). Key properties include:
- The vertices are the endpoints of the major axis.
- The distance from the center to each focus is the eccentricity.
- The general equation of an ellipse with center at (h,k) is (x-h)^2/a^2 + (y-k)^2/b^2 = 1.
- Examples are provided to illustrate finding the equation of an ellipse given properties like the foci, vertices, or axes.

Conic sectioins

This document defines and provides the standard forms of conic sections, including circles, ellipses, parabolas, and hyperbolas. It explains that a circle is a closed loop where each point is a fixed distance from the center. A parabola is the set of points equidistant from a directrix and focus. An ellipse is the set of points where the sum of distances to two foci is constant. A hyperbola is the set of points where the difference between distances to two foci is constant. Standard forms are provided for each conic section with the vertex or center at (0,0) or (h,k) and characteristics like vertices and foci.

ellipse (An Introduction)

An ellipse is a curve where the sum of the distances from two fixed focal points is a constant. It is defined as the set of all points whose distances from two focal points add up to a constant. The standard equation of an ellipse is (x/a)^2 + (y/b)^2 = 1, where the focal points are located at (±c,0) and the vertices are located at (±a,0) and covertices at (0,±b). Examples are given of finding the focal points, vertices, and covertices of ellipses with given standard equations and of writing the standard equation of an ellipse given its focal points and constant sum of distances.

Conic Sections- Circle, Parabola, Ellipse, Hyperbola

Conic Sections- Circle, Parabola, Ellipse, Hyperbola all topics covered. this is a presentation with excelent animations and explatition.

Lesson 8 conic sections - parabola

The document defines conic sections and describes parabolas. It provides specific objectives related to defining conic sections, identifying different types, describing parabolas, and converting between general and standard forms of parabola equations. It then gives details on the focus, directrix, vertex, latus rectum, and eccentricity of parabolas. Examples of problems involving finding parabola equations and properties from conditions are also provided.

CONIC SECTIONS AND ITS APPLICATIONS

This document defines and provides examples of different types of conic sections - parabolas, ellipses, and hyperbolas. It explains that conic sections are curves formed by the intersection of a plane with a cone, and that points on a conic section have a fixed ratio between their distance to a focus point and its directrix line, known as eccentricity. Eccentricity values distinguish the different conic section types. Examples of each in diagrams and applications like planetary orbits, bicycle gears, and network synchronization are also provided.

Parabola

The document discusses parabolas and their key properties:
- A parabola is the set of all points equidistant from a fixed line called the directrix and a fixed point called the focus.
- The standard equation of a parabola depends on the orientation of its axis and vertex.
- Key properties include the axis of symmetry, direction of opening, and the length of the latus rectum.

Pre-Calculus: Conics - Introduction to Conics and Determining & Graphing Circ...

This PowerPoint contains an introduction to conical sections: the conics formed from double-napped circular cone - the Parabola, Hyperbola, Circle, & Ellipse. It also contains the basic parts of Circle. Identifying the standard form of circle's radius and center. Graphing a circle from its standard form. Transforming General Equation of Circle to Standard Form and some of the special cases.

Properties of circle

Some properties of tangents, secants and chords, Angles formed by intersecting chords, tangent and chord and two secants, Chords and their arcs, Segments of chords secants and tangents, Lengths of arcs and areas of sectors

Ellipse

An ellipse is a curve in a plane where the sum of the distances to two fixed points (foci) is a constant. The two foci, along with the major and minor axes and vertices, are used to define an ellipse. The standard equation of an ellipse depends on whether the foci lie along the x-axis or y-axis. Key properties including eccentricity and the latus rectum are also described.

Ellipse

An ellipse is defined algebraically as the set of all points where the sum of the distances to two fixed points (the foci) is a constant. Geometrically, an ellipse can be constructed by stretching a circle: using a piece of string fixed at both ends (the foci) and tracing the path of a pencil as it is moved around so that the total length of string remains constant.
The standard equation of an ellipse is (x-h)2/a2 + (y-k)2/b2 = 1, where (h,k) is the center and a and b are the lengths of the semi-major and semi-minor axes. To graph an ellipse, one plots

Equations of circles

This document discusses graphing circles and converting between graphing form and standard form equations of circles. It provides examples of writing the equation of a circle given its center and radius in graphing form. It also shows how to find the center, radius, and equation of a circle given the standard form equation. The key points are:
- In graphing form, the center is denoted as (h, k) and the equation is (x - h)2 + (y - k)2 = r2
- To convert to standard form, complete the square and factor the left side, moving any constant to the right side.

6.14.1 Arcs, Chords, and Angles

This document defines key terms and concepts related to circles, arcs, chords, and tangents. It defines circles, diameters, radii, central angles, secants, chords, tangents, and points of tangency. It presents theorems about perpendicular lines being tangent to a circle, congruent tangent segments, and radii/diameters bisecting chords and arcs. Examples demonstrate finding measures of arcs and angles, and calculating lengths based on circle properties.

Equation of Hyperbola

The document provides information about hyperbolas including:
- A hyperbola is defined as the set of all points where the difference between the distances to two fixed points (foci) is a constant.
- Key properties include two foci, a transverse axis connecting the foci, a conjugate axis perpendicular to the transverse axis, and vertices where it intersects the transverse axis.
- The standard equation of a hyperbola with foci on the x-axis is (y2/b2) - (x2/a2) = 1, where a and b are related to the distances between the foci and vertices.

parabola class 12

This document discusses parabolas, including their key features like the vertex, focus, directrix, and axis of symmetry. It provides examples of how to graph parabolas given their standard form equations, both for parabolas with vertices at the origin and for parabolas with other vertices. It also shows how to write the standard form equation of a parabola when given its focus and directrix.

Quadratic functions

The document discusses quadratic functions and their graphs. It defines quadratic functions as functions of the form f(x)=ax^2+bx+c, where a is not equal to 0. The graph of a quadratic function is a parabola with certain characteristics: it is symmetrical about an axis of symmetry and has a vertex which is either a maximum or minimum point. The axis of symmetry is the line x=0 for functions of the form f(x)=ax^2 and the vertex is at (0,0). For functions of the form f(x)=ax^2+k, the graph is a translation of f(x)=ax^2, so the vertex is (0,k) and the

Ellipse

This document discusses analytic geometry and ellipses. It begins with objectives of defining key terms of conic sections like ellipses, and solving equations and real-world problems involving ellipses. An activity is described where students can draw an ellipse using a rubber band stretched between two pins. Examples of completed ellipses are shown along with their equations and key properties labeled like foci, vertices, axes, and eccentricity. Students are given practice problems to find properties of ellipses based on given information.

Parabola

The document discusses parabolas and their key properties:
- A parabola is defined as the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
- The vertex is the point where the axis of symmetry intersects the parabola. The focus and directrix are a fixed distance (p) from the vertex.
- The latus rectum is the line segment from the focus to the parabola, perpendicular to the axis of symmetry. Its length is determined by the equation of the parabola.

class 10 circles

- A circle is the set of all points in a plane that are equidistant from a fixed point called the center.
- Important terms related to circles include chord, diameter, arc, sector, minor/major segments.
- A tangent touches the circle at one point, a secant intersects at two points, and there can be at most two parallel tangents for a given secant.
- The tangent radius theorem states that the tangent is perpendicular to the radius at the point of contact. The equal tangent lengths theorem says tangents from an external point are equal in length.

Conic sections

This document discusses conic sections, including circles, ellipses, parabolas, and hyperbolas. It provides:
1) The definitions and standard equations of each conic section, describing how they are formed from the intersection of a plane with a double cone.
2) Examples of different forms the equations can take and the geometric properties of each conic section, such as foci, axes, vertices, and asymptotes.
3) Methods for writing the equations of tangents to conics and using parametric equations to represent loci.
In less than 3 sentences, it summarizes the key information about conic sections provided in the document.

Lesson 9 conic sections - ellipse

Lesson 9 conic sections - ellipse

Conic sectioins

Conic sectioins

ellipse (An Introduction)

ellipse (An Introduction)

Conic Sections- Circle, Parabola, Ellipse, Hyperbola

Conic Sections- Circle, Parabola, Ellipse, Hyperbola

Lesson 8 conic sections - parabola

Lesson 8 conic sections - parabola

CONIC SECTIONS AND ITS APPLICATIONS

CONIC SECTIONS AND ITS APPLICATIONS

Parabola

Parabola

Pre-Calculus: Conics - Introduction to Conics and Determining & Graphing Circ...

Pre-Calculus: Conics - Introduction to Conics and Determining & Graphing Circ...

Properties of circle

Properties of circle

Ellipse

Ellipse

Ellipse

Ellipse

Equations of circles

Equations of circles

6.14.1 Arcs, Chords, and Angles

6.14.1 Arcs, Chords, and Angles

Equation of Hyperbola

Equation of Hyperbola

parabola class 12

parabola class 12

Quadratic functions

Quadratic functions

Ellipse

Ellipse

Parabola

Parabola

class 10 circles

class 10 circles

Conic sections

Conic sections

Paso 4_Álgebra, trigonometría y Geometría Analítica

The document discusses different types of conic sections including circles, ellipses, hyperbolas, and parabolas. It provides the general equation for conic sections and the conditions to determine which type of conic section is represented based on the values of certain coefficients in the equation. It then gives the standard forms of the equations for each type of conic section and discusses some of their defining geometric properties.

math conic sections.pptx

This document discusses parabolas as a type of conic section. It defines key properties of parabolas including the vertex, focal length, latus rectum, and directrix. The standard and vertex forms of the parabolic equation are presented. Methods for graphing parabolas by plotting points from an equation are described. An example problem calculates the depth of a satellite dish with a parabolic cross-section given its width and the distance to the focus. Real-world applications of parabolas in satellite dishes, heaters, and arched structures are briefly mentioned.

Maths project

This document summarizes different conic sections including the parabola, ellipse, and hyperbola. It provides the definitions and key properties of each shape. For parabolas, it describes that any point is at an equal distance from the focus and directrix, and provides the standard equation of y2 = 4ax. For ellipses, it defines them as points whose sum of the distances to two fixed points is a constant, and gives the standard equation of x2/a2 + y2/b2 = 1. For hyperbolas, it describes them as points where the ratio of the distances to the focus and directrix are constant, and provides the standard equation of x2/a2 - y

Pre c alc module 1-conic-sections

The document provides an overview of Module 1 of an analytic geometry course, which covers conic sections. Lesson 1 focuses specifically on circles. It defines a circle, discusses the standard form of a circular equation, and how to graph circles. It also provides an example of stating the center and radius of a circle given its equation. The objectives are to illustrate different conic sections including circles, define and work with circular equations, and solve problems involving circles.

Conic_Sections_Hyperbolas FCIT compat.ppt

The document discusses hyperbolas. It begins by providing an algebraic definition of a hyperbola as the set of points where the difference between the distances to two fixed points (foci) is a constant. It then provides steps for graphing a hyperbola from its standard form equation, including identifying the center, vertices, transverse/conjugate axes, asymptotes, and foci. Examples of graphing hyperbolas are shown.

Plano Numérico

The document describes key concepts related to the Cartesian plane including:
- The Cartesian plane consists of two perpendicular axes (x and y) intersecting at the origin point.
- Points on the plane are represented as ordered pairs (x,y).
- The distance between two points P1(x1,y1) and P2(x2,y2) is given by the formula d = √(x2 - x1)2 + (y2 - y1)2.
- Circles, parabolas, ellipses, and hyperbolas are examples of curves that can be represented on the Cartesian plane using algebraic equations. Their properties and equations are discussed.

Plano numerico

This document defines and explains key concepts in analytic geometry including:
- The Cartesian plane consisting of perpendicular x and y axes intersecting at the origin.
- Distances between points on the plane and formulas to calculate distances.
- Midpoint of a segment and properties of circles like radius, diameter, and equations of circles.
- Elements and equations of parabolas, ellipses, and hyperbolas including vertices, foci, axes, and canonical forms.
- René Descartes is credited with developing analytic geometry which uses the Cartesian plane.

Lecture co2 math 21-1

This document provides information about circles and conic sections. It begins with an overview of circles, including definitions of key terms like radius, diameter, chord, and equations of circles given the center and radius or three points. It then covers conic sections, defining ellipses, parabolas and hyperbolas based on eccentricity. Equations of various conic sections are derived based on the location of foci, directrix, vertex and other geometric properties. Sample problems are provided to demonstrate solving problems involving different geometric configurations of circles and conic sections.

Conic Sections Parabolas FCIT compat.ppt

The document discusses the geometric and algebraic definitions of a parabola, noting that a parabola is the set of all points equidistant from a fixed point (the focus) and a line (the directrix). It also provides steps for writing the standard form equation of a parabola given its vertex and focus, as well as for graphing a parabola by plotting its vertex, focus, directrix, axis of symmetry, and sketching the curve through these points.

Ellipse.pptx

1. The document defines an ellipse and its key properties including its standard equation form. It discusses how an ellipse is a set of points where the sum of the distances to two fixed points (foci) is constant.
2. Parts of an ellipse like its vertices, covertices, axes, and directrices are defined. The standard equation of an ellipse centered at the origin is derived.
3. Examples are provided of determining the coordinates of foci, vertices, covertices, and directrices from equations. Problems involving finding equations or properties given certain conditions are also presented.

114333628 irisan-kerucut

The document discusses properties of parabolas, including their definition as the set of points equidistant from a focus point and directrix line. It presents the standard equation for a par

114333628 irisan-kerucut

The document discusses properties and equations of circles, including the standard form of a circle equation with a given center and radius. It also discusses tangent lines to circles, providing the process and equations for finding the equation of a tangent line to a circle at a given

lesson4.-ellipse f.pptx

This document provides an overview of ellipses in pre-calculus. It defines an ellipse as a set of points where the sum of the distances from two fixed points (foci) is constant. Key properties of ellipses are described, including the relationship between the major axis, minor axis, foci, vertices, and covertices. Several examples are worked through, sketching ellipses from equations in standard form and determining characteristic points. Practice problems are provided to identify variables in equations and find standard forms.

g11.pptx

The document defines and discusses parabolas. A parabola is the set of all points equidistant from a fixed point called the focus and a line called the directrix. The key parts of a parabola are identified as the vertex, focus, directrix, axis of symmetry, and latus rectum. An algebraic definition and process for graphing a parabola given its equation is provided. An example parabola with the equation (x - 5)2 = 12(y – 6) is graphed step-by-step as an illustration.

Plano numerico

Plano numerico
distancia
Punto medio
Ecuaciones de la recta
Circunferencia
Parabola
Elipse
Hiperbola

Plano numerico

Plano numerico
distancia
Punto medio
Ecuaciones de la recta
Circunferencia
Parabola
Elipse
Hiperbola

Unit 13.5

This document discusses hyperbolas, including:
1) Hyperbolas are defined as sets of points where the difference between the distances to two fixed points (foci) is a constant. They can be graphed using the standard form equation.
2) Hyperbolas have two branches, two axes of symmetry, vertices, co-vertices, and asymptotes. The standard form equation depends on whether the transverse axis is horizontal or vertical.
3) Examples show how to write the standard form equation, find vertices/co-vertices/asymptotes, and graph hyperbolas. Parameters like the center, foci and axes can change the graph of the hyperbola.

parabola.pdf parabola القطع المكافئ math

This document discusses parabolas and their key properties and applications. It begins by introducing parabolas as sets of points equidistant from a fixed line called the directrix and a fixed point called the focus. The standard form of a parabola equation is presented. Properties of parabolas including the vertex, axis of symmetry, focus, and directrix are described. Applications where parabolic shapes are used such as suspension bridges, vehicle headlights, and satellite dishes are also mentioned. Parabolas are widely used to model projectile motion and in optical systems where their reflective properties help focus or direct light.

Actividad colaborativa 551108 20

This document provides information about ellipses, hyperbolas, parabolas, and circles. It defines key elements of each curve such as foci, vertices, axes, and directrix. It also presents the standard equation for each curve in both canonical form (centered at the origin) and general form (shifted center). Examples are given of shifting the coordinates to obtain equations for non-canonical curves.

Plano numérico

(Distancia. Punto Medio. Ecuaciones y trazado de circunferencias, Parábolas, elipses, hipérbola. Representar gráficamente las ecuaciones de las cónicas).

Paso 4_Álgebra, trigonometría y Geometría Analítica

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math conic sections.pptx

math conic sections.pptx

Maths project

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Conic_Sections_Hyperbolas FCIT compat.ppt

Conic_Sections_Hyperbolas FCIT compat.ppt

Plano Numérico

Plano Numérico

Plano numerico

Plano numerico

Lecture co2 math 21-1

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Conic Sections Parabolas FCIT compat.ppt

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114333628 irisan-kerucut

114333628 irisan-kerucut

114333628 irisan-kerucut

114333628 irisan-kerucut

lesson4.-ellipse f.pptx

lesson4.-ellipse f.pptx

g11.pptx

g11.pptx

Plano numerico

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Unit 13.5

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parabola.pdf parabola القطع المكافئ math

parabola.pdf parabola القطع المكافئ math

Actividad colaborativa 551108 20

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Plano numérico

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Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...

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Educational Technology in the Health Sciences

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How to Manage Reception Report in Odoo 17

A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.

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It outlines the basic identity elements such as symbol, logotype, colors, and typefaces. It provides examples of applying the identity to materials like letterhead, business cards, reports, folders, and websites.

HYPERTENSION - SLIDE SHARE PRESENTATION.

IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
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These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.

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The document discuss about the hospitals and it's organization .

Information and Communication Technology in Education

(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 2)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐈𝐂𝐓 𝐢𝐧 𝐞𝐝𝐮𝐜𝐚𝐭𝐢𝐨𝐧:
Students will be able to explain the role and impact of Information and Communication Technology (ICT) in education. They will understand how ICT tools, such as computers, the internet, and educational software, enhance learning and teaching processes. By exploring various ICT applications, students will recognize how these technologies facilitate access to information, improve communication, support collaboration, and enable personalized learning experiences.
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐫𝐞𝐥𝐢𝐚𝐛𝐥𝐞 𝐬𝐨𝐮𝐫𝐜𝐞𝐬 𝐨𝐧 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐫𝐧𝐞𝐭:
-Students will be able to discuss what constitutes reliable sources on the internet. They will learn to identify key characteristics of trustworthy information, such as credibility, accuracy, and authority. By examining different types of online sources, students will develop skills to evaluate the reliability of websites and content, ensuring they can distinguish between reputable information and misinformation.

220711130082 Srabanti Bag Internet Resources For Natural Science

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With Metta,
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The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.

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FinalSD_MathematicsGrade7_Session2_Unida.pptx

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Data Structure using C by Dr. K Adisesha .ppsx

220711130083 SUBHASHREE RAKSHIT Internet resources for social science

220711130083 SUBHASHREE RAKSHIT Internet resources for social science

- 1. CONIC SECTIONS By: Jasmin Joyce M. Terrado Candice P. Madrid
- 2. DEFINITIONS Conic Section: Any figure that can be formed by slicing a double cone with a plane Parabola Circle Ellipse Hyperbola
- 3. EQUATION OF A CONIC SECTION 2 2 0 where A, B, and C are not all zero. Ax Bxy Cy Dx Ey F
- 4. DISTINCT PROPERTIES OF CONIC SECTIONS Parabola: A = 0 OR C = 0 Circle: A = C Ellipse: , but both have the same sign Hyperbola: A and C have Different signs A C
- 5. 1. CIRCLE A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. Standard Form: x² + y² = r² You can determine the equation for a circle by using the distance formula then applying the standard form equation. Or you can use the standard form. Most of the time we will assume the center is (0,0). If it is otherwise, it will be stated. It might look like: (x-h)² + (y – k)² = r²
- 6. II. PARABOLA A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ), and. a fixed straight line (the directrix ) STANDARD EQUATION OF A PARABOLA: Let the vertex be (h, k) and p be the distance between the vertex and the focus and p ≠ 0. (x−h)2=4p(y−k) (x−h)2=-4p(y−k)vertical axis; directrix is y = k - p (y−k)2=4p(x−h) (y−k)2=- 4p(x−h) horizontal axis; directrix is x = h - p
- 7. III. ELLIPSE An ellipse is an important conic section and is formed by intersecting a cone with a plane that does not go through the vertex of a cone. The ellipse is defined by two points, each called a focus. From any point on the ellipse, the sum of the distances to the focus points is constant. The position of the foci determine the shape of the ellipse. STANDARD EQUATION OF AN ELLIPSE:
- 8. IV. HYPERBOLA A hyperbola is the set of all points in a plane such that the absolute value of the difference of the distances between two fixed points stays constant. The two given points are the foci of the hyperbola, and the midpoint of the segment joining the foci is the center of the hyperbola.