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: 19


The graph is shown below

Work Step by Step

$5{{x}^{2}}+5{{y}^{2}}=125$ …… (1) Multiply $\frac{1}{5}$on both the sides of the equation $5{{x}^{2}}+5{{y}^{2}}=125$. Identifying $a\text{ and }b$ in equation: $\begin{align} & \frac{5}{5}{{x}^{2}}+\frac{5}{5}{{y}^{2}}=\frac{125}{5} \\ & {{x}^{2}}+{{y}^{2}}=25 \\ \end{align}$ Equation ${{x}^{2}}+{{y}^{2}}=25$ is an equation of a circle. Since $a=5\text{ and }b=5$, the x-intercepts are $\left( -5,0 \right)\text{ and }\left( 5,0 \right)$ and the y-intercepts are$\left( 0,-5 \right)\text{ and }\left( 0,5 \right)$. Plot this point and connect them with the oval shaped curve.
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