Stitz-Zeager_College_Algebra_e-book

# Since we have found a solution the system is

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 &lt; c, we get a2 &lt; 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...
View Full Document

## 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.

Ask a homework question - tutors are online