Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 4 - 4.3 - Conics - 4.3 Exercises - Page 339: 67



Work Step by Step

Transverse axis is horizontal. $(±c,0)=(±10,0)$ $c=10$ The equation of the asymptotes when transverse axis is horizontal: $y=±\frac{a}{b}x$ The equation of the asymptotes: $y=±\frac{3}{4}x$ So: $\frac{a}{b}=\frac{3}{4}$ $a=\frac{3}{4}b$ $a^2=\frac{9}{16}b^2$ $c^2=a^2+b^2=\frac{9}{16}b^2+b^2=\frac{25}{16}b^2$ $100=\frac{25}{16}b^2$ $b^2=\frac{1600}{25}=64$ $a^2=\frac{9}{16}·64=36$ Standard form when transverse axis is horizontal: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ $\frac{x^2}{36}-\frac{y^2}{64}=1$
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