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This document discusses applications of various conic sections in real life. It begins by defining conic sections as curves derived from slicing a double-napped cone and lists the main types - parabolas, ellipses, circles, and hyperbolas. It then provides examples of applications for each type of conic section, such as parabolas in football trajectories, ellipses in eye shapes and planet orbits, circles in wheels and records, and hyperbolas in sonic booms and lighthouse beams. The document aims to illustrate how conic sections appear frequently in architecture, engineering, and natural phenomena.

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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.

introduction to functions grade 11(General Math)

This document contains:
1. An outline for a mathematics course covering functions and their graphs, basic business mathematics, and logic.
2. Lessons on identifying functions from relations, evaluating functions, and representing real-life situations using functions including piecewise functions.
3. Examples of evaluating functions, operations on functions, and determining whether a relation is a function based on its graph or ordered pairs.
4. An activity drilling students on identifying functions versus non-functions.

Conic sections in daily life

this talks about the real life applications of conic sections namely circle, parabola, hyperbola and ellipse.
art integrated project for class 11 maths - CBSE

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.

Hyperbolas

This document provides information about hyperbolas including:
- Hyperbolas have two branches and two vertices, with the foci further from the center than the vertices.
- The fundamental properties of a hyperbola include its center, vertices, foci, transverse axis, and the relationship between a, b, and c.
- Hyperbolas can be graphed using their standard form equations, with the equation varying depending on the orientation of the transverse axis.
- Asymptotes are straight lines that the branches of the hyperbola curve towards at increasing distance from the center.
- Properties like eccentricity describe the amount of curvature in hyperbolas.

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.

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.

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.

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.

introduction to functions grade 11(General Math)

This document contains:
1. An outline for a mathematics course covering functions and their graphs, basic business mathematics, and logic.
2. Lessons on identifying functions from relations, evaluating functions, and representing real-life situations using functions including piecewise functions.
3. Examples of evaluating functions, operations on functions, and determining whether a relation is a function based on its graph or ordered pairs.
4. An activity drilling students on identifying functions versus non-functions.

Conic sections in daily life

this talks about the real life applications of conic sections namely circle, parabola, hyperbola and ellipse.
art integrated project for class 11 maths - CBSE

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.

Hyperbolas

This document provides information about hyperbolas including:
- Hyperbolas have two branches and two vertices, with the foci further from the center than the vertices.
- The fundamental properties of a hyperbola include its center, vertices, foci, transverse axis, and the relationship between a, b, and c.
- Hyperbolas can be graphed using their standard form equations, with the equation varying depending on the orientation of the transverse axis.
- Asymptotes are straight lines that the branches of the hyperbola curve towards at increasing distance from the center.
- Properties like eccentricity describe the amount of curvature in hyperbolas.

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.

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.

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.

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.

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.

Representing Real-Life Situations Using Rational Function

This document discusses polynomial and rational functions. It provides examples of polynomial functions in the forms of p(x) = 5t^5 - 2t^3 + 7t and a rational function representing drug concentration over time of the form c(t) = 5t/(t^2+1). It also shows a table of values for the rational function for t = 1, 2, 5, 10 that is used to graph the relationship.

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.

Rational Equations and Inequalities

This document discusses solving rational equations and inequalities. It begins with definitions of rational equations and inequalities. Examples are provided to demonstrate how to solve rational equations by multiplying both sides by the least common denominator to eliminate fractions. The document notes that extraneous solutions may arise and must be checked. Methods for solving rational inequalities using graphs, tables, and algebra are presented. Practice problems are included for students to test their understanding.

GENERAL MATHEMATICS Module 1: Review on Functions

This document provides an overview of key concepts related to functions, including:
- Definitions of functions and relations.
- Examples of functions represented as ordered pairs, tables, and graphs.
- Evaluating functions by inputting values for variables.
- Determining the domain and range of functions.
- Performing operations on functions like addition, subtraction, multiplication, and composition.
- Identifying whether functions are even, odd, or neither based on their behavior when the variable x is replaced by -x.

Theorems on limits

This presentation introduces limits and provides examples of applying 8 theorems of limits. It begins with an introduction explaining that calculus and limits are challenging topics for college students. It then covers the definitions of limits and 8 theorems for evaluating different types of limits, including limits of constants, variables, products, quotients, and composite functions. Example problems demonstrate how to use each theorem to find the limit as the variable approaches a value. The presentation aims to make solving limits easier by explaining the theorems.

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.

Rational function representation

This document discusses rational functions and provides examples of representing rational functions through tables of values, graphs, and equations. It defines a rational function as a function of the form f(x) = p(x)/q(x) where p(x) and q(x) are polynomials and q(x) is not the zero function. Examples are given of using rational functions to model speed as a function of time for running a 100-meter dash and calculating winning percentages in a basketball league.

General Mathematics - Rational Functions

It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its zeroes. It is also comprised of some examples and exercises to be done for the said topic.

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This document provides an overview of a Teaching Guide for a General Physics 1 course for senior high school. It outlines the course content standards and performance standards, which are mapped to specific learning competencies. The course covers units, measurement, vectors, one-dimensional kinematics including uniformly accelerated motion, and two-dimensional and three-dimensional motion. The Teaching Guide is designed to be highly usable for teachers, providing classroom activities and notes to help develop students' understanding, mastery, and ownership of the content.

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This document is the learner's material for precalculus developed by the Department of Education of the Philippines. It was collaboratively developed by educators from public and private schools. The document contains the copyright notice and details that it is the property of the Department of Education and may not be reproduced without their permission. It provides the table of contents that outlines the units and lessons covered in the material.ย

Barayti ng wika

barayti ng wika

Basic calculus

This document provides an overview and table of contents for a textbook on basic calculus. It discusses the purpose and structure of the book, which aims to explain key concepts in calculus through examples and exercises. The book covers topics like limits, derivatives, integrals, and their applications. It also includes a chapter reviewing prerequisite algebra and geometry topics to refresh students' knowledge before beginning calculus. The overview explains how each chapter builds upon the previous ones to develop an understanding of calculus.

Lesson 1 INTRODUCTION TO FUNCTIONS

The document defines functions and relations. It reviews basic math operations and introduces the concepts of relations, inputs and outputs, domains and ranges. A relation is a correspondence between two sets, while a function is a special type of relation where each input has a single, unique output. Functions can be illustrated through sets of ordered pairs, mapping diagrams, and graphs where the vertical line test determines if a relation is a function. Students are given examples of relations and functions to identify which are functions.

Mathematics in the Modern World Lecture 1

The document discusses how patterns and mathematics are present in nature. It provides examples of symmetry in butterflies and starfish and discusses how hexagonal structures allow for better packing than squares, as bees use in honeycombs. The document also discusses other examples of mathematics in nature, including Turing's explanation of animal coat patterns and the presence of the Fibonacci sequence in flowers and shells. It provides examples of using exponential growth models to determine past and future population sizes.

Chapter i

The document provides an outline for a lesson on functions and relations. It includes:
- A review of functions as machines, tables of values, graphs, and the vertical line test.
- How functions can represent real-life situations, including piecewise functions.
- An example of using a piecewise function to model the temperature of water as heat is added.
- The lesson aims to represent real-life situations using functions and solve problems involving functions.

Statistics and probability lesson 1

This document provides an introduction to statistics and the statistical process. It discusses how statistics involves using data to answer questions or solve problems. Questions are classified as either set A, which have a definite factual answer, or set B, which require collecting and analyzing data. The statistical process is outlined as planning data collection, collecting quality data, summarizing the data, and using summaries to make evidence-based decisions or conclusions. Examples of questions that can and cannot be answered using this process are provided.

Solving rational inequalities

The document discusses solving rational inequalities. It defines interval and set notation that can be used to represent the solutions to inequalities. It then presents the procedure for solving rational inequalities, which involves rewriting the inequality as a single fraction on one side of the inequality symbol and 0 on the other side, and determining the intervals where the fraction is positive or negative. Examples are provided to demonstrate solving rational inequalities and applying the solutions to word problems.

Operations on Functions

To find the sum of two functions f and g, add the corresponding terms of f(x) and g(x). To find the difference, subtract the terms of g(x) from f(x), distributing the negative sign. To find the product, multiply corresponding terms using FOIL. To find the quotient, divide the functions. The composition f o g means to substitute g(x) for each x in f(x). The domain of a composition is numbers where g(x) is in the domain of f.

Conic Sections (Class 11 Project)

This document is a mathematics project submitted by Kushagra Agrawal to Kamal Soni Sir. It includes an acknowledgement thanking Kamal Soni Sir for providing guidance. The project contains information on different types of conic sections (parabolas, ellipses, hyperbolas, and circles) including their definitions, common features, examples, and applications. It also discusses the latus rectum and eccentricity of conic sections. The project was created using PowerPoint and includes references.

conicsection-230210095242-c864bbb3.pdf m

This document is a mathematics project submitted by Swastik Subham Pattnaik to Rajashree Ma'am. It includes an acknowledgements section thanking those who provided guidance. The project consists of a PowerPoint presentation on conic sections, including definitions of parabolas, ellipses, hyperbolas, and circles. It discusses their common features like foci and directrices. Applications of each type of conic section are also presented, along with explanations of latus rectum and eccentricity.

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.

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.

Representing Real-Life Situations Using Rational Function

This document discusses polynomial and rational functions. It provides examples of polynomial functions in the forms of p(x) = 5t^5 - 2t^3 + 7t and a rational function representing drug concentration over time of the form c(t) = 5t/(t^2+1). It also shows a table of values for the rational function for t = 1, 2, 5, 10 that is used to graph the relationship.

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.

Rational Equations and Inequalities

This document discusses solving rational equations and inequalities. It begins with definitions of rational equations and inequalities. Examples are provided to demonstrate how to solve rational equations by multiplying both sides by the least common denominator to eliminate fractions. The document notes that extraneous solutions may arise and must be checked. Methods for solving rational inequalities using graphs, tables, and algebra are presented. Practice problems are included for students to test their understanding.

GENERAL MATHEMATICS Module 1: Review on Functions

This document provides an overview of key concepts related to functions, including:
- Definitions of functions and relations.
- Examples of functions represented as ordered pairs, tables, and graphs.
- Evaluating functions by inputting values for variables.
- Determining the domain and range of functions.
- Performing operations on functions like addition, subtraction, multiplication, and composition.
- Identifying whether functions are even, odd, or neither based on their behavior when the variable x is replaced by -x.

Theorems on limits

This presentation introduces limits and provides examples of applying 8 theorems of limits. It begins with an introduction explaining that calculus and limits are challenging topics for college students. It then covers the definitions of limits and 8 theorems for evaluating different types of limits, including limits of constants, variables, products, quotients, and composite functions. Example problems demonstrate how to use each theorem to find the limit as the variable approaches a value. The presentation aims to make solving limits easier by explaining the theorems.

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.

Rational function representation

This document discusses rational functions and provides examples of representing rational functions through tables of values, graphs, and equations. It defines a rational function as a function of the form f(x) = p(x)/q(x) where p(x) and q(x) are polynomials and q(x) is not the zero function. Examples are given of using rational functions to model speed as a function of time for running a 100-meter dash and calculating winning percentages in a basketball league.

General Mathematics - Rational Functions

It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its zeroes. It is also comprised of some examples and exercises to be done for the said topic.

GENERAL PHYSICS 1 TEACHING GUIDE

This document provides an overview of a Teaching Guide for a General Physics 1 course for senior high school. It outlines the course content standards and performance standards, which are mapped to specific learning competencies. The course covers units, measurement, vectors, one-dimensional kinematics including uniformly accelerated motion, and two-dimensional and three-dimensional motion. The Teaching Guide is designed to be highly usable for teachers, providing classroom activities and notes to help develop students' understanding, mastery, and ownership of the content.

Pre calculus Grade 11 Learner's Module Senior High School

Pre calculus Grade 11 Learner's Module Senior High SchoolMarinduque National High School, Marinduque State College

This document is the learner's material for precalculus developed by the Department of Education of the Philippines. It was collaboratively developed by educators from public and private schools. The document contains the copyright notice and details that it is the property of the Department of Education and may not be reproduced without their permission. It provides the table of contents that outlines the units and lessons covered in the material.ย

Barayti ng wika

barayti ng wika

Basic calculus

This document provides an overview and table of contents for a textbook on basic calculus. It discusses the purpose and structure of the book, which aims to explain key concepts in calculus through examples and exercises. The book covers topics like limits, derivatives, integrals, and their applications. It also includes a chapter reviewing prerequisite algebra and geometry topics to refresh students' knowledge before beginning calculus. The overview explains how each chapter builds upon the previous ones to develop an understanding of calculus.

Lesson 1 INTRODUCTION TO FUNCTIONS

The document defines functions and relations. It reviews basic math operations and introduces the concepts of relations, inputs and outputs, domains and ranges. A relation is a correspondence between two sets, while a function is a special type of relation where each input has a single, unique output. Functions can be illustrated through sets of ordered pairs, mapping diagrams, and graphs where the vertical line test determines if a relation is a function. Students are given examples of relations and functions to identify which are functions.

Mathematics in the Modern World Lecture 1

The document discusses how patterns and mathematics are present in nature. It provides examples of symmetry in butterflies and starfish and discusses how hexagonal structures allow for better packing than squares, as bees use in honeycombs. The document also discusses other examples of mathematics in nature, including Turing's explanation of animal coat patterns and the presence of the Fibonacci sequence in flowers and shells. It provides examples of using exponential growth models to determine past and future population sizes.

Chapter i

The document provides an outline for a lesson on functions and relations. It includes:
- A review of functions as machines, tables of values, graphs, and the vertical line test.
- How functions can represent real-life situations, including piecewise functions.
- An example of using a piecewise function to model the temperature of water as heat is added.
- The lesson aims to represent real-life situations using functions and solve problems involving functions.

Statistics and probability lesson 1

This document provides an introduction to statistics and the statistical process. It discusses how statistics involves using data to answer questions or solve problems. Questions are classified as either set A, which have a definite factual answer, or set B, which require collecting and analyzing data. The statistical process is outlined as planning data collection, collecting quality data, summarizing the data, and using summaries to make evidence-based decisions or conclusions. Examples of questions that can and cannot be answered using this process are provided.

Solving rational inequalities

The document discusses solving rational inequalities. It defines interval and set notation that can be used to represent the solutions to inequalities. It then presents the procedure for solving rational inequalities, which involves rewriting the inequality as a single fraction on one side of the inequality symbol and 0 on the other side, and determining the intervals where the fraction is positive or negative. Examples are provided to demonstrate solving rational inequalities and applying the solutions to word problems.

Operations on Functions

To find the sum of two functions f and g, add the corresponding terms of f(x) and g(x). To find the difference, subtract the terms of g(x) from f(x), distributing the negative sign. To find the product, multiply corresponding terms using FOIL. To find the quotient, divide the functions. The composition f o g means to substitute g(x) for each x in f(x). The domain of a composition is numbers where g(x) is in the domain of f.

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CONIC SECTIONS AND ITS APPLICATIONS

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Ellipse

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

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

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Rational Equations and Inequalities

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GENERAL MATHEMATICS Module 1: Review on Functions

GENERAL MATHEMATICS Module 1: Review on Functions

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Theorems on limits

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Conic section Maths Class 11

Conic section Maths Class 11

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Rational function representation

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General Mathematics - Rational Functions

General Mathematics - Rational Functions

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GENERAL PHYSICS 1 TEACHING GUIDE

GENERAL PHYSICS 1 TEACHING GUIDE

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Pre calculus Grade 11 Learner's Module Senior High School

Pre calculus Grade 11 Learner's Module Senior High School

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Barayti ng wika

Barayti ng wika

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Basic calculus

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Lesson 1 INTRODUCTION TO FUNCTIONS

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Mathematics in the Modern World Lecture 1

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Chapter i

Chapter i

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Statistics and probability lesson 1

Statistics and probability lesson 1

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Solving rational inequalities

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Operations on Functions

Operations on Functions

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Conic Sections (Class 11 Project)

This document is a mathematics project submitted by Kushagra Agrawal to Kamal Soni Sir. It includes an acknowledgement thanking Kamal Soni Sir for providing guidance. The project contains information on different types of conic sections (parabolas, ellipses, hyperbolas, and circles) including their definitions, common features, examples, and applications. It also discusses the latus rectum and eccentricity of conic sections. The project was created using PowerPoint and includes references.

conicsection-230210095242-c864bbb3.pdf m

This document is a mathematics project submitted by Swastik Subham Pattnaik to Rajashree Ma'am. It includes an acknowledgements section thanking those who provided guidance. The project consists of a PowerPoint presentation on conic sections, including definitions of parabolas, ellipses, hyperbolas, and circles. It discusses their common features like foci and directrices. Applications of each type of conic section are also presented, along with explanations of latus rectum and eccentricity.

Conic Section.pptx

This document is a mathematics project submitted by Swastik Subham Pattnaik to Rajashree Ma'am. It includes an acknowledgements section thanking those who provided guidance. The project consists of a PowerPoint presentation on conic sections, including definitions of parabolas, ellipses, hyperbolas, and circles. It discusses their common features like foci and directrices. Applications of each type of conic section are also presented, along with explanations of latus rectum and eccentricity.

STRAND 3.0 FORCE AND ENERGY.pptx CBC FOR LEARNERS

STRAND 3.0 FORCE AND ENERGY.pptx

Curves in Engineering

The document discusses various types of curves that are important in engineering applications. It covers conic sections like ellipses, parabolas and hyperbolas. It also discusses roulettes like cycloids and trochoids that are generated by a point on a moving circle. Involutes, which are curves traced by a point unwinding from a circle, are also covered. Examples are provided of how these curves are used in civil, mechanical and electrical engineering applications.

Curvesstandard 091013005307-phpapp01

The document discusses various types of curves that are important in engineering applications. It covers conic sections like ellipses, parabolas and hyperbolas. It also discusses roulettes like cycloids and trochoids as well as involutes. Specific examples of curves covered in detail include the cycloid, referred to as the "quarrel curve", epicycloids, hypotrochoids and the involute of a circle. The document emphasizes the importance of understanding these curves for various engineering disciplines like civil, mechanical and electrical engineering.

calculus.pptx

This presentation provides an overview of conic sections including the parabola, ellipse, and hyperbola. It begins with an introduction defining conic sections as curves formed by the intersection of a plane and a right circular cone. The three basic types of conic sections - parabola, ellipse, and hyperbola - are then defined. Examples of applications are given for each type of conic section, including using parabolas for cannon aiming in medieval times, elliptical orbits of planets, and the hyperbolic shape of guitar bodies.

Light - Reflection or Refraction

A full-fledge explanation of Reflection and Refraction Phenomenon, topic wise in understandable language.

Ones own work

Parabolas are U-shaped curves that appear in many real-world contexts. Some examples of parabolas in everyday life include satellite dishes, which use the reflective properties of parabolas to focus signals to a receiver; headlights, which focus beams of light using a parabolic mirror; suspension bridges, whose cable shapes resemble parabolic curves; and the path of any object thrown upwards, such as a ball or water from a fountain, which traces a parabolic trajectory.

1-ELLIPSE.pptx

The Kaybiang Tunnel is the longest elliptical shaped tunnel in the Philippines, connecting two towns. An ellipse is the set of all points in a plane where the sum of the distances from two fixed points, called foci, is a constant. The Kaybiang Tunnel has an elliptical shape with its longest section piercing through a mountain.

Optical telescope

in this presentation analyzing optical telescope and type of lens then lens telescope compared newton telescope in university of sulaimani. tell me for other description.

Engineering Curves

This document provides information about cycloidal curves. It defines different types of cycloidal curves that are generated when a circle rolls along a straight line or another circle without slipping. These include cycloids, epicycloids, and hypocycloids. The document outlines the classification of these curves and provides step-by-step instructions for constructing cycloids, epicycloids, and hypocycloids using compasses. It concludes with some applications of cycloidal curves in gear design, conveyors, and mechanical mechanisms.

06 lecture outline

Telescopes allow astronomers to observe the cosmos in different wavelengths of light. Ground-based telescopes are limited by Earth's atmosphere, so many telescopes have been placed in space. There are two main types of telescopes - refracting and reflecting - with most large professional telescopes being reflecting designs. Multiple telescopes can work together using interferometry to achieve higher angular resolution comparable to a single larger telescope. Astronomers use telescopes to take images of celestial objects, perform spectroscopy to analyze light, and monitor changes over time.

06 lecture outline

Telescopes allow astronomers to observe the universe in different wavelengths of light. Ground-based telescopes are limited by Earth's atmosphere, so many telescopes have been placed in space. There are two main types of telescopes - refracting telescopes which use lenses and reflecting telescopes which use mirrors. Multiple telescopes can work together using interferometry to achieve the resolution of a larger single telescope. Astronomers use telescopes to take images of celestial objects, perform spectroscopy to analyze light, and monitor changes over time.

ENGINEERING CURVES.docx

The document discusses the applications of ellipses, parabolas, and hyperbolas in three paragraphs. Ellipses are used in architecture and furniture design. Parabolas are used in antennas, microphones, car headlights, and missiles due to their reflective properties. Hyperbolas are used in guitar design, satellite systems, lenses, and monitors due to their optical properties. The document also provides methods for constructing ellipses, parabolas, and hyperbolas.

Opticsandlight

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- 1. Applications of conic sections โขParabola โขEllipse โขCircle โขHyperbola
- 3. Submitted To: Maโm Sapna Makhdoom Submitted By: โขIrum GulBahar 02 โขHajrah Majeed 14 โขHumera Yousaf 19 โขAmna Ayub 21 Topic: Applications of Conic Sections in Real/Daily Life Session: 2013-17 Department: Mathematics Mirpur University Of Science & Technology (MUST)
- 4. โข Dedication: We dedicate this project name โ Applications of Conic sections in real Lifeโ to our parents and Family members.
- 5. โข Abstract In this project we discuss โApplications of Conic Sections in Real Lifeโ. There are a lot of uses of conic sections in real life. we have discussed only some.
- 6. โข Acknowledgement First of all we would like to thank Allah almighty for making this project possible for us. Then special thanks to Maโm Sapna Makhdoom for helping us in completing this project
- 7. Definition: โ Conic sections are the curves which can be derived from taking slices of a โdouble- nappedโ cone. โ OR โA section or a slice through A cone.โ โ OR A conic section is a figure formed by the intersection of a plane and a circular cone. Depending on the angle of the plane with respect to the cone.
- 8. Types Of conic Sections โข Parabola โข Ellipse โข Circle โข Hyperbola Hyperbola Parabola Ellipse Circle
- 9. A little history: Conic sections date back to Ancient Greece and was thought to discovered by Menaechmus around 360-350 B.C. What eventually resulted in the discovery of conic sections began with a simple problem. It is believed that the great king Minos wanted to build a Tomb of his son, Glaucus, but felt that his tomb was too small. This was later deemed โDoubling the cubeโ. Menaechmus was at that time and a student of Eudoxus, a famous Greek scholar. To solve the case of โdoubling the cubeโ he focused on mean proportions and the use of construction of a cone. Eventually his solution became known as โConic sectionsโ.
- 10. World Applications โข Conic sections are used by architects and architectural engineers. They can be seen in wide variety in the world in buildings, churches, and arches.
- 11. Parabola: โข A set of all the points in the plane equidistant from a given fixed point and a given fixed line in the plane is a parabola. โ The fixed point is focus. โ The fixed line is the directrix.
- 12. Applications of Parabola o Parabolas are everywhere in modern society. Parabolas can be found in most things we encounter everyday. parabolas are formed when a football is kicked, a baseball is hit, a basketball hoop is made, dolphins jump and much more. ๏ผ The bottom of Eiffel Tower is a Parabola and it can be interpreted as a negative parabola as it opens down. ๏ผ Parabola is the path of any object thrown in the air and is the mathematical curve used by engineers in designing some suspension bridges. The properties of parabola make it the ideal shape for reflector of an automobile headlight.
- 13. โข Parabola was used back in the medieval period with the use of cannons and cannon balls. Armies used parabolas to navigate the path of a cannon ball to attack the enemy. โข The swing set are like parabolas because of their U shape. โข The ST. louis was designed in the shape of parabola. โข Gallilo was the first person to show tha the path of an object thrown in the space is a parabola
- 14. โข Two Parabolas connect to make the Mcdonaldโs M. โข It is also used when making roller coasters because the points that connect the roller coaster are the same distance away from the focus, it is able to create a parabola that is concave down.
- 15. Ellipse: โข An ellipse is the set of all points in the plane, the sum of whose distances from two fixed points is a given positive constant that is greater than the distance between the fixed points.
- 16. Application of Ellipse: โข Ellipse are contributed to the real world because of Oval shape. โข Tilt a glass of water and the surface of the liquid acquires an elliptical outline. โข The Tycho Brahe plantarium is located in Denmark.this building takes the form of an ellipse and it is clearly shown. Any cylinder sliced at an angle will reveal an ellipse. โข Footballs are elliptic.
- 17. โข Your eye is an ellipse! It is a horizontal ellipse, the eye ball can be considered the center and the surrounding shape forms an ellipse, the minor axis is vertical and the major axis is horizontal across the eye. The two ends of the eye can be considered as vertex. โข Bicycle chain is an example of ellipse. โข Earth orbit around the sun is an ellipse. Without the orbit we all .
- 18. โข The ellipse is found in the rotation of planets in solar system. All planets orbit around the sun creates an ellipse.
- 19. Circle: โข Definition: ๏ง A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre).
- 20. Applications of circles: โข Most, if not all, clocks are circular. โข Ferris wheels are circular. โข Mostly Pizzaโs are circle. โข Conic sections are every where shown by water ripples from these rain drops.
- 21. โข Gears and records along with CDโs are ideal examples of circles in real life. They are, and were in their time, essential to every day life. โข Bangles and Rings are examples of circle โข Circles are used in real life situation as wheels on cars bikes and other forms of transportation. The shape of a circle helps create a smooth movement for a car or a bike to move from place to place. โข Doughnut is a perfect example of a circle. The shape is prime factorization of the delicacy. It allows a baker to induce a heat distribution to create an evenly backed delicious doughnut.
- 22. Hyperbola: โข Definition: ๏ผ A hyperbola is the set of all points in the plane, the difference of whose distances from two fixed distinct points is given a positive constant that is less than the distance between them.
- 23. Applications of Hyperbola โข In the architecture of the James S Mcdonell planetarium, a hyperbola is formed. โข When you turn a lamp on, you get a hyperbola, if the the lamp is open from the top and the bottom the light comes out and form a hyperbola. The asymptote can be seen coming out from top and the bottom.
- 24. โข In Nuclear cooling towers the hyperbolic shape is used due to its due to its ability to withstand high winds, while also making it in the most efficient was possible. โข A glass lens uses light contraction to magnify objects. Light is reflected in and out of the lens in a hyperbolic way creating a zoom.
- 25. โข Radio waves and hyperbolas can be used in navigation. If the centre of each circle gives out a radio signal then the signals will intersect each other in hyperbolas. This is how hyperbolic radio navigation systems were created.
- 26. A sonic boom shock wave has the shape of a cone, and it intersects the ground in part of a hyperbola. It hits every point on this curve at the same time, so that people in different places along the curve on the ground hear it at the same time. Because the airplane is moving forward, the hyperbolic curve moves forward and eventually the boom can be heard by everyone in its path.