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: 75

Answer

Vertices: $(0,±1)$ Asymptotes: $y=±\frac{1}{2}x$
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Work Step by Step

Standard form when transverse axis is vertical: $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ $2y^2-\frac{x^2}{2}=2$ $\frac{y^2}{1}-\frac{x^2}{4}=1$ $a^2=1$ $a=1$ $b^2=4$ $b=2$ Vertices when transverse axis is vertical: $(0,±a)=(0,±1)$ Asymptotes when transverse axis is vertical: $y=±\frac{a}{b}x$ $y=±\frac{1}{2}x$
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