Answer
The graph is shown below
Work Step by Step
$4{{x}^{2}}+9{{y}^{2}}=36$ …… (1)
Multiply $\frac{1}{36}$on both the sides of equation $4{{x}^{2}}+9{{y}^{2}}=36$.
Identifying $a\text{ and }b$ in the equation,
$\begin{align}
& \frac{4}{36}{{x}^{2}}+\frac{9}{36}{{y}^{2}}=\frac{36}{36} \\
& \frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1 \\
& \frac{{{x}^{2}}}{{{\left( 3 \right)}^{2}}}+\frac{{{y}^{2}}}{{{\left( 2 \right)}^{2}}}=1
\end{align}$
Since ${{a}^{2}}>{{b}^{2}}$, the ellipse will be horizontal.
Since $a=3\text{ and }b=2$, the x-intercepts are $\left( -3,0 \right)\text{ and }\left( 3,0 \right)$ and the y-intercepts are $\left( 0,-2 \right)\text{ and }\left( 0,2 \right)$.
Plot this point and connect them with the oval shaped curve.
