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: 45

Answer

asymptotes $y=\pm4(x+2)-1$ foci: $(-2,-1\pm\frac{\sqrt {17}}{2})$
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Work Step by Step

Step 1. Rewriting the equation as $16(x^2+4x+4)-(y^2+2y+1)=64-1-67=-4$ or $\frac{(y+1)^2}{4}-\frac{(x+2)^2}{1/4}=1$ we have $a=2,b=\frac{1}{2}, c=\sqrt {a^2+b^2}=\frac{\sqrt {17}}{2}$ centered at $(-2,-1)$ with a vertical transverse axis. Step 2. We can find the vertices as $(-2,-3),(-2,1)$ and asymptotes as $y+1=\pm\frac{a}{b}(x+2)$ or $y=\pm4(x+2)-1$ Step 3. We can graph the equation as shown in the figure with foci at $(-2,-1\pm\frac{\sqrt {17}}{2})$
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