Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 9 - Section 9.2 - The Hyperbola - Exercise Set - Page 981: 14


See graph; foci $(\pm\sqrt {41},0)$; asymptotes $y=\pm\frac{5}{4}x$

Work Step by Step

Step 1. From the given equation $\frac{x^2}{16}-\frac{y^2}{25}=1$, we have $a=4, b=5, c=\sqrt {a^2+b^2}=\sqrt {41}$ centered at $(0,0)$ with a horizontal transverse axis. Step 2. We can find the vertices as $(\pm4,0)$ and asymptotes as $y=\pm\frac{5}{4}x$ Step 3. We can graph the equation as shown in the figure with foci at $(\pm\sqrt {41},0)$
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