Post8o2_1330 - Section 8.2 Ellipses An ellipse is the set...

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1 Section 8.2 Ellipses An ellipse is the set of all points, the sum of whose distances from two fixed points is constant. Each fixed point is called a focus (plural = foci ). Basic “Vertical” Ellipse (centers at origin) : Basic “vertical” ellipse : Equation: 2 2 2 2 1 x y b a + = , a b Foci: (0, ) c ± , where 2 2 2 c a b = - Vertices: (0, ) a ± Eccentricity: c e a = The eccentricity provides a numerical measure of how much the ellipse deviates from being a circle. The eccentricity e is a number between 0 and 1. Basic “Horizontal” Ellipse : Equation: 2 2 2 2 1 x y a b + = , a b Foci: ( ,0) c ± , where 2 2 2 c a b = - Vertices: ( ,0) a ± Eccentricity: c e a = For ellipses, the line segment joining the vertices is called the Major Axis (length 2a) and the line segment through the center and perpendicular to the major axis with endpoints on the ellipse is called the Minor Axis (length 2b) . -a
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Post8o2_1330 - Section 8.2 Ellipses An ellipse is the set...

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