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