HYPERBOLAS IN STANDARD POSITION (0, c) (-c, 0) (c, 0) -b --- (0, -c) The derivations of these equations are similar to those already given for parabolas and ellipses, so we will leave them as exercises. However, to illustrate how the equations of the asymptotes are derived, we will derive those equations for the hyperbola

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter7: Conic Sections
Section7.1: Parabolas
Problem 37E
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Derive the equation (x²/a²)−(y²/b²) = 1 given in Figure 10.4.22.

HYPERBOLAS IN STANDARD POSITION
(0, c)
(-c, 0)
(c, 0)
-b
---
(0, -c)
The derivations of these equations are similar to those already given for parabolas and
ellipses, so we will leave them as exercises. However, to illustrate how the equations of
the asymptotes are derived, we will derive those equations for the hyperbola
Transcribed Image Text:HYPERBOLAS IN STANDARD POSITION (0, c) (-c, 0) (c, 0) -b --- (0, -c) The derivations of these equations are similar to those already given for parabolas and ellipses, so we will leave them as exercises. However, to illustrate how the equations of the asymptotes are derived, we will derive those equations for the hyperbola
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