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: 79

Answer

Vertices: $(±\frac{1}{3},0)$ Asymptotes: $y=±3x~~$ (Black lines)
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Work Step by Step

Standard form when transverse axis is horizontal: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ $9x^2-y^2=1$ $\frac{x^2}{\frac{1}{9}}-\frac{y^2}{1}=1$ $a^2=\frac{1}{9}$ $a=\frac{1}{3}$ $b^2=1$ $b=1$ Vertices when transverse axis is horizontal: $(±a,0)=(±\frac{1}{3},0)$ Asymptotes when transverse axis is horizontal: $y=±\frac{b}{a}x=±\frac{1}{\frac{1}{3}}x$ $y=±3x$
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