Stitz-Zeager_College_Algebra_e-book

Since we have found a solution the system is

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Unformatted text preview: t (x, y ) on the hyperbola. Applying Definition 7.6, we get distance from (−c, 0) to (x, y ) − distance from (c, 0) to (x, y ) = 2a (x − (−c))2 + (y − 0)2 − (x − c)2 + (y − 0)2 = 2a (x + c)2 + y 2 − (x − c)2 + y 2 = 2a Using the same arsenal of Intermediate Algebra weaponry we used in deriving the standard formula of an ellipse, Equation 7.4, we arrive at the following.1 1 It is a good exercise to actually work this out. 436 Hooked on Conics a2 − c2 x2 + a2 y 2 = a2 a2 − c2 What remains is to determine the relationship between a, b and c. To that end, we note that since a and c are both positive numbers with a < c, we get a2 < c2 so that a2 − c2 is a negative number. Hence, c2 − a2 is a positive number. For reasons which will become clear soon, we re-write the equation by solving for y 2 /x2 to get a2 − c2 x2 + a2 y 2 − c2 − a2 x2 + a2 y 2 a2 y 2 y2 x2 = a2 a2 − c2 = −a2 c2 − a2 = c2 − a2 x2 − a2 c2 − a2 c2 − a2 c2 − a2 = − a2 x2 c2 − a2 c2 − a2 y2 → 0 so that 2 → . By setting x2...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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