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Conic Sections Anyway you slice it
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Properties of Cone generate cone
A cone is created by rotating a line called the generator around an axis. The greater the slope of the line the skinnier the cone generate cone
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Definition: A conic section is the intersection of a plane and a Double Cone. By changing the angle and location of intersection, we can produce 1. circle, 2. ellipse, 3. parabola 4. hyperbola;
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How to get Shapes 1. plane perpendicular to axis of cone – circle (horizontal plane) 2. not perpindicular only intersect one nappe – A. ellipse B. Parabola – parallel to generating line 3. plane intersecting both nappes – hyperbola Slice cone
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Equations of Conic Sections
General Equation of all conic sections We will examine different forms of this quadratic relation
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Equation in Vertex Form
Circle Ellipse Parabola Hyperbola
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Translations (h, k) Center (vertex)
Circle Ellipse Parabola Hyperbola
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Parabola – only 1 variable squared
Hyperbola – both variables squared, different coefficients (divided by different numbers) and subtracted Circle – both variables squared, addition – coeffecients same Ellipse – both variables squared, addition, coefficients different (divided by different numbers)
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Conics in Real Life Ellipse Hyperbola Parabola Circle
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Degenerate Conic Sections
Point – horizontal plane cuts cone at vertex Line – plane cuts the cone exactly on the generator Intersecting Lines – plane cuts the cone exactly on the vertical axis
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