Answer
The graph is shown below
Work Step by Step
$3{{x}^{2}}+3{{y}^{2}}=48$ …… (1)
Multiply $\frac{1}{3}$on both the sides of equation $3{{x}^{2}}+3{{y}^{2}}=48$.
Identifying $a\text{ and }b$ in equation.
$\begin{align}
& \frac{3}{3}{{x}^{2}}+\frac{3}{3}{{y}^{2}}=\frac{48}{3} \\
& {{x}^{2}}+{{y}^{2}}=16
\end{align}$
Equation ${{x}^{2}}+{{y}^{2}}=16$ is an equation of a circle.
Since $a=4\text{ and }b=4$, the x-intercepts are $\left( -4,0 \right)\text{ and }\left( 4,0 \right)$ and the y-intercepts are$\left( 0,-4 \right)\text{ and }\left( 0,4 \right)$.
Plot this point and connect them with the oval shaped curve.
