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: 68



Work Step by Step

Transverse axis is vertical. $(0,±c)=(0,±8)$ $c=8$ The equation of the asymptotes when transverse axis is vertical: $y=±\frac{a}{b}x$ The equation of the asymptotes: $y=±4x$ So: $\frac{a}{b}=4$ $a=4b$ $a^2=16b^2$ $c^2=a^2+b^2=16b^2+b^2=17b^2$ $64=17b^2$ $b^2=\frac{64}{17}$ $a^2=16(\frac{64}{17})=\frac{1024}{17}$ Standard form when transverse axis is vertical: $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ $\frac{y^2}{\frac{1024}{17}}-\frac{x^2}{\frac{64}{17}}=1$ $\frac{17y^2}{1024}-\frac{17x^2}{64}=1$
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