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: 56

Answer

see graph; domain $(-\infty,\infty)$, range $(-\infty,-2]\cup[2,\infty)$
1585158910

Work Step by Step

Step 1. From the given equation $\frac{(y)^2}{4}-\frac{(x)^2}{25}=1$, we have $a=2, b=5, c=\sqrt {a^2+b^2}=\sqrt {29}$ centered at $(0,0)$ with a vertical transverse axis. Step 2. We can find the vertices as $(0,\pm2)$, foci as $(0,\pm\sqrt {29})$, and asymptotes as $y=\frac{a}{b}(x)$ or $y=\pm\frac{2}{5}(x)$ Step 3. We can graph the equation as shown in the figure with domain $(-\infty,\infty)$ and range $(-\infty,-2]\cup[2,\infty)$
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