College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 7 - Review Exercises - Page 540: 2


Hyperbola. Vertices: $ \quad (5,0), \quad (-5,0)$ Foci: $ \quad (\sqrt{26},0), \quad (-\sqrt{26},0)$ Asymptotes: $ \displaystyle \quad y=\frac{1}{5}x, \quad y=-\frac{1}{5}x$

Work Step by Step

Both variables squared, a minus between terms$\Rightarrow$hyperbola $\displaystyle \frac{x^{2}}{5^{2}}-\frac{y^{2}}{1}=1$ Table 4: $\begin{array}{cccc} {\text{Foci}}&{\text { Vertices }}&{\text{Equation}}&{\text{asymptotes}}\\\hline (h\pm c,k)&{(h \pm a, k)}&{ \displaystyle \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1,}&{b^{2}=c^{2}-a^{2}\displaystyle \quad y-k=\pm\frac{b}{a}(x-h)}\end{array}$ $a=5,\quad b=1, \quad $Find $c$ $c^{2}=a^{2}+b^{2}=25+1=26$ $c=\sqrt{26}$ Vertices: $ \quad (h \pm a, k)=(0\pm 5,0),$ Foci: $ \quad (h\pm c,k)=(0\pm\sqrt{26},0),$ Asymptotes: $ \displaystyle \quad y-k=\pm\frac{b}{a}(x-h)$ $y=\displaystyle \pm\frac{1}{5}(x)$
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