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 982: 36

Answer

asymptotes: $y=\pm\frac{5}{3}(x+2)$ foci: $(-2\pm\sqrt {34},0)$
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Work Step by Step

Step 1. From the given equation $\frac{(x+2)^2}{9}-\frac{(y)^2}{25}=1$, we have $a=3, b=5, c=\sqrt {a^2+b^2}=\sqrt {34}$ centered at $(-2,0)$ with a horizontal transverse axis. Step 2. We can find the vertices as $(-5,0),(1,0),(-2,-5),(-2,5)$ and asymptotes as $y=\frac{b}{a}(x+2)$ or $y=\pm\frac{5}{3}(x+2)$ Step 3. We can graph the equation as shown in the figure with foci at $(-2\pm\sqrt {34},0)$
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