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It can also be considered an equation in 117

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Unformatted text preview: − c)2 − (x + c)2 4a2 − 4cx a2 − cx a2 − cx 2 a4 − 2a2 cx + c2 x2 a4 − 2a2 cx + c2 x2 a4 − a2 c2 a2 a2 − c2 We are nearly finished. Recall that b2 = a2 − c2 so that a2 − c2 x2 + a2 y 2 = a2 a2 − c2 b2 x2 + a2 y 2 = a2 b2 x2 y 2 +2 =1 a2 b 1 In other words, tons and tons of Intermediate Algebra. Stay sharp, this is not for the faint of heart. 422 Hooked on Conics This equation is for an ellipse centered at the origin. If the ellipse were centered at a point (h, k ), we would get the following Equation 7.4. The Standard Equation of an Ellipse: For positive unequal numbers a and b, the equation of an ellipse with center (h, k ) is (x − h)2 (y − k )2 + =1 a2 b2 Some remarks about Equation 7.4 are in order. First note that the values a and b determine how far in the x and y directions, respectively, one counts from the center to arrive at points on the ellipse. Also take note that if a > b, then we have an ellipse whose major axis is horizontal, and hence, the foci lie to the l...
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