College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 7 - Conic Sections - Exercise Set 7.2 - Page 685: 15

Answer

Asymptotes: $y=\displaystyle \pm\frac{4}{5}x .$ Foci: $(2\sqrt{41}, 0)$ and $(-2\sqrt{41}, 0)$.

Work Step by Step

The hyperbola $\displaystyle \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ has a horizontal transverse axis and two asymptotes $y=\displaystyle \frac{b}{a}x$ and $y=-\displaystyle \frac{b}{a}x$. ----------- $a=10, \quad b=8$ For the foci, $c^{2}=a^{2}+b^{2}=100+64=164$ $ c=2\sqrt{41}\approx$12.806 Vertices: $(10,\ 0)$ and $(-10,0)$. Asymptotes: $y=\displaystyle \pm\frac{8}{10}x =\displaystyle \pm\frac{4}{5}x .$ Foci: $(2\sqrt{41}, 0)$ and $(-2\sqrt{41}, 0)$.
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