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There are four types of conic sections: parabolas, circles, hyperbolas, and ellipses. Conic sections are formed by the intersection of a plane and a cone. The parabola has a U-shaped graph and its equation is Y=X^2. Circles are defined by the equation (x-a)^2 + (y-b)^2 = r^2, where a and b are the x and y coordinates of the center and r is the radius. Hyperbolas have the form a^2/x^2 - b^2/y^2 = 1. Ellipses use the same parameters a and b as circles and hyperbolas in their equation.
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- Rules for working with fractions, percentages, equations, inequalities, sequences, and conversions.
introduction to conics
A conic is the intersection of a plane and a right circular cone. The four basic types of conics are parabolas, ellipses, circles, and hyperbolas. All conics can be represented by the standard quadratic equation Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 and classified based on the values of the coefficients. Analytic geometry studies geometric shapes using the coordinate plane and formulas for their graphs, with a focus on the conics represented by the standard quadratic equation.
PARABOLA VS HYPERBOLA.pptx
This document compares and contrasts parabolas and hyperbolas. It begins with brief introductions to each type of curve. It then discusses their histories, definitions, general equations, eccentricities, latus recta, and applications. Parabolas are defined as curves where all points are equidistant from a focus and directrix. Hyperbolas are formed by the intersection of a plane and two cones, where the difference between distances to two foci is constant. The document provides formulas for the general equations, eccentricities, and latus recta of both parabolas and hyperbolas. Finally, it notes applications of parabolas in reflection and hyperbolas in technologies like telescopes.
Forms Of Quadratic
The document discusses three forms of quadratic functions: standard form f(x)=ax^2+bx+c, vertex form f(x)=a(x-h)^2+k, and intercept form f(x)=a(x-p)(x-q). For each form, it provides the key characteristics: for standard form the vertex is (-b/2a, f(-b/2a)) and the y-intercept is c; for vertex form the vertex is (h,k); and for intercept form the x-intercepts are (p,0) and (q,0) and the y-intercept is apq. It also gives instructions for graphing each form of quadratic function
Quadrilaterals
This document defines and describes properties of different types of quadrilaterals. It states that quadrilaterals are four-sided polygons, and defines parallelograms as quadrilaterals with both pairs of opposite sides parallel. Properties of parallelograms include having congruent opposite sides and angles. Rectangles are defined as parallelograms with four right angles, while squares are rectangles with four congruent sides. Rhombuses are parallelograms with four congruent sides. Trapezoids have one pair of parallel sides. Formulas are provided for calculating areas of parallelograms, triangles, trapezoids and other shapes.
Hyperbola
A hyperbola is an open curve formed by the intersection of a plane and a double cone. It has two branches that resemble infinite bows and are mirror images of each other. The hyperbola is defined such that for any point on the curve, the difference between the distances to its two foci is a constant. It can be described using equations involving its foci, vertices, and asymptotes. The eccentricity measures how curved the hyperbola is, with larger values indicating straighter branches.
Maths PPT on parabola Class 11.pptx
A parabola is a set of points equidistant from a fixed line (the directrix) and a fixed point (the focus) not on the line. The key properties of a parabola include its focus, directrix, vertex, axis, and latus rectum. There are four types of parabolas defined by the position of the vertex and axis. Parabolas have many applications in fields like antennas, microphones, vehicle headlights, and ballistics due to their shape.
Maths porject work - quadrilaterals - nihal gour
This document discusses different types of quadrilaterals. It defines a quadrilateral as a polygon with four sides and provides definitions for specific types including trapezoids, parallelograms, rectangles, rhombuses, squares, and kites. It also includes a taxonomic classification chart showing the relationships between different quadrilaterals and provides some properties of parallelograms, rectangles, rhombuses, and squares.
quadrilaterals
1) A quadrilateral is a polygon with four sides and four vertices. There are over 9 million types of quadrilaterals that can be classified based on their properties.
2) Key types of quadrilaterals include parallelograms, rectangles, rhombi, squares, trapezoids, trapezoids, and kites. Parallelograms have two sets of parallel sides, while rectangles have four right angles. Squares have all the properties of rectangles and rhombi.
3) Important theorems about quadrilaterals include that the sum of the interior angles is always 360 degrees and that the midpoint of a side of a triangle is parallel to the opposite side
Mathsproject quadrilaterals
1) A quadrilateral is a polygon with four sides and four vertices. There are over 9 million types of quadrilaterals that can be classified as simple or complex.
2) Quadrilaterals include parallelograms, trapezoids, kites, and more. A parallelogram has two sets of parallel sides and opposite/adjacent angles are equal. A square is a special type of rectangle and parallelogram.
3) The interior angles of any quadrilateral sum to 360 degrees. The line segment between the midpoints of two sides of a triangle is parallel to the third side and half its length.
Conic Sections- Circle, Parabola, Ellipse, Hyperbola
Conic Sections- Circle, Parabola, Ellipse, Hyperbola all topics covered. this is a presentation with excelent animations and explatition.
Similar to Ben c conic sections (20)
Conic Sections- Circle, Parabola, Ellipse, Hyperbola
Conic Sections- Circle, Parabola, Ellipse, Hyperbola
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Ben c conic sections
- 1. Conic Sections By Ben Clayton
- 2. A Conicare four types of Section is when a There Parabola plane and a cone Conic Sections intersect. This is When The plane is perpendicular to the Long edge of the cone
- 3. Parabola The a graph this is what On shape you would see is shown below you would see.
- 4. The Maths part of Parabola Equation: Y=X² Translation in the x and y Direction: Y=(X – a)² + B A Being The X translation with the opposite sign B Being The y Translation with the same sign.
- 5. Circles Equation: (x-a) ² + (y-b) ² = r² A is the x Coordinate of the centre with the opposite sign B is the Y Coordinate of the centre with the opposite sign R is the Radius of the circle R (A,B)
- 6. Hyperbole x y Equation: a b
- 7. Ellipses Equation: A and B are exactly the same as the Circle and hyperbola (See Handout)
- 8. Bye