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: 17


The graph is shown below

Work Step by Step

$2{{x}^{2}}+3{{y}^{2}}=6$ …… (1) Multiply $\frac{1}{6}$on both the sides of equation $2{{x}^{2}}+3{{y}^{2}}=6$. Identifying $a\text{ and }b$ in equation. $\begin{align} & \frac{2}{6}{{x}^{2}}+\frac{3}{6}{{y}^{2}}=\frac{6}{6} \\ & \frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{2}=1 \\ & \frac{{{x}^{2}}}{{{\left( \sqrt{3} \right)}^{2}}}+\frac{{{y}^{2}}}{{{\left( \sqrt{2} \right)}^{2}}}=1 \end{align}$ Since ${{a}^{2}}>{{b}^{2}}$, the ellipse will be horizontal. Since $a=\sqrt{3}\text{ and }b=\sqrt{2}$, the x-intercepts are $\left( -\sqrt{3},0 \right)\text{ and }\left( \sqrt{3},0 \right)$ and the y-intercepts are $\left( 0,-\sqrt{2} \right)\text{ and }\left( 0,\sqrt{2} \right)$. Plot these points and connect them with the oval shaped curve.
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