Answer
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.
