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

$2{{x}^{2}}+3{{y}^{2}}=6$ …… (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.