Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Cumulative Review: 37

Answer

Refer to the graph below.
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Work Step by Step

RECALL: The graph of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is a horizontal hyperbola that has: center at $(0,0)$ vertices: $(a, 0)$ and $(-a, 0)$ asymptotes: $y=(\frac{b}{a})x$ and $y=-(\frac{b}{a})x$ The given equation can be written as:$\dfrac{x^2}{4^2} - \dfrac{y^2}{5^2}=1$. Thus, iwith $a=4$ and $b=5$, its graph is a hyperbola with: center: $(0, 0)$ vertices: $(-4, 0)$ and $(4, 0)$ asymptotes: $y=-\frac{5}{4}x$ and $y=\frac{5}{4}x$ To graph the given hyperbola, perform the following steps: (1) Plot the vertices $(-4, 0)$ and $(4, 0)$. (2) Sketch tje asymptotes $y=-\frac{5}{4}x$ and $y=\frac{5}{4}x$ using broken lines (because they are not really part of the graph, they only serve as asymptotes of the hyperbola). (3) Sketch the hyperbola by graphing two curves passing through the vertices and asymptotic to the lines in step (2) above, Refer to the graph in the answer part above.
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