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: 66



Work Step by Step

Transverse axis is vertical. $(0,±a)=(0,±3)$ $a=3$ The equation of the asymptotes when transverse axis is vertical: $y=±\frac{a}{b}x$ The equation of the asymptotes: $y=±3x$ So: $\frac{a}{b}=3$ $\frac{3}{b}=3$ $b=1$ Standard form when transverse axis is vertical: $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ $\frac{y^2}{3^2}-\frac{x^2}{1^2}=1$ $\frac{y^2}{9}-\frac{x^2}{1}=1$ $\frac{y^2}{9}-x^2=1$
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