Answer
Intercepts: $(-2,0), (2,0), (0,-3)$, and $(0,3)$.
The graph has x-axis, y-axis, and origin symmetry.
Work Step by Step
$\left[\begin{array}{ll}
\text{x-intercepts:} & \text{y-intercepts:}\\
9x^{2}+4(0)^{2}=36 & 9(0)^{2}+4y^{2}=36\\
9x^{2}=36 & 4y^{2}=36\\
x^{2}=4 & y^{2}=9\\
x=\pm 2 & y=\pm 3
\end{array}\right]$
Intercepts: $(-2,0), (2,0), (0,-3)$, and $(0,3)$.
Test x-axis symmetry: Replace $y$ with $-y$
$9x^{2}+4(-y)^{2}=36$
$9x^{2}+4y^{2}=36$ ...same as initial equation
Test y-axis symmetry: Replace $x$ with $-x$
$9 (-x)^{2}+4y^{2}=36$
$9x^{2}+4y^{2}=36$ ...same as initial equation
Test origin symmetry: $x\rightarrow-x$ and $y\rightarrow-y$.
$9 (-x)^{2}+4y^{2}=36$
$9x^{2}+4y^{2}=36$ ...same as initial equation