Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 16


$$ \left(\frac{x}{3}\right)^{2}-\left(\frac{y}{3/2}\right)^{2}=1. $$

Work Step by Step

Since the vertices are $(\pm 3,0)$ and the asymptotes are $y=\pm \frac{1}{2}x$, then we have $a=3, \frac{b}{a}=\frac{b}{3}=\frac{1}{2} $, and hence $b=\frac{3}{2} $. Hence, the equation of the hyperbola is given by $$ \left(\frac{x}{3}\right)^{2}-\left(\frac{y}{3/2}\right)^{2}=1. $$
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