Answer
The graph is shown below
Work Step by Step
$9{{x}^{2}}+16{{y}^{2}}=144$ …… (1)
Multiply $\frac{1}{144}$on both the sides of equation $9{{x}^{2}}+16{{y}^{2}}=144$.
Identifying $a\text{ and }b$ in the equation,
$\begin{align}
& \frac{9}{144}{{x}^{2}}+\frac{16}{144}{{y}^{2}}=\frac{144}{144} \\
& \frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1 \\
& \frac{{{x}^{2}}}{{{\left( 4 \right)}^{2}}}+\frac{{{y}^{2}}}{{{\left( 3 \right)}^{2}}}=1
\end{align}$
Since ${{a}^{2}}>{{b}^{2}}$, the ellipse will be horizontal.
Since $a=4\text{ and }b=3$, the x-intercepts are $\left( -4,0 \right)\text{ and }\left( 4,0 \right)$ and the y-intercepts are $\left( 0,-3 \right)\text{ and }\left( 0,3 \right)$.
Plot these points and connect them with the oval shaped curve.
