Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 13 - Conic Sections - 13.2 Conic Sections: Ellipses - 13.2 Exercise Set - Page 861: 6


False statement

Work Step by Step

Identify $a\text{ and }b$ in equation $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{9}=1$. $\frac{{{x}^{2}}}{{{\left( 5 \right)}^{2}}}-\frac{{{y}^{2}}}{{{\left( 3 \right)}^{2}}}=1$ Since ${{a}^{2}}>{{b}^{2}}$, the equation of the hyperbola will be horizontal. Since $a=5\text{ and }b=3$, the x-intercepts are $\left( -5,0 \right)\text{ and }\left( 5,0 \right)$ and the y-intercepts are $\left( 0,-3 \right)\text{ and }\left( 0,3 \right)$. Plot the points and connect them with the oval shape curve. Thus, the equation $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{9}=1$, so it is a false statement.
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