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

$5{{x}^{2}}+7{{y}^{2}}=35$ …… (1) Multiply $\frac{1}{35}$on both the sides of equation $5{{x}^{2}}+7{{y}^{2}}=35$. Identifying $a\text{ and }b$ in equation. \begin{align} & \frac{5}{35}{{x}^{2}}+\frac{7}{35}{{y}^{2}}=\frac{35}{35} \\ & \frac{{{x}^{2}}}{7}+\frac{{{y}^{2}}}{5}=1 \\ & \frac{{{x}^{2}}}{{{\left( \sqrt{7} \right)}^{2}}}+\frac{{{y}^{2}}}{{{\left( \sqrt{5} \right)}^{2}}}=1 \end{align} Since ${{a}^{2}}>{{b}^{2}}$, the ellipse will be horizontal. Since $a=\sqrt{7}\text{ and }b=\sqrt{5}$, the x-intercepts are $\left( -\sqrt{7},0 \right)\text{ and }\left( \sqrt{7},0 \right)$ and the y-intercepts are$\left( 0,-\sqrt{5} \right)\text{ and }\left( 0,\sqrt{5} \right)$. Plot this point and connect them with the oval shaped curve.