Answer
$(\pm2,0), (0,\pm3)$,
symmetric with respect to the x-axis, the y-axis, and the origin.
Work Step by Step
Step 1. For x-intercept(s), let $y=0$, we have $x^2=4\longrightarrow (\pm2,0)$, for y-intercept(s), let $x=0$, we have $y^2=9\longrightarrow (0,\pm3)$,
Step 2. To test for x-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $9(x)^2+4(-y)^2=36$ which is the same as the original equation, thus it is symmetric with respect to the x-axis,
Step 3. To test for y-axis symmetry, replace $(x,y)$ with $(-x,y)$, we have $9(-x)^2+4(y)^2=36$ which is the same as the original equation, thus it is symmetric with respect to the y-axis,
Step 4. To test for origin symmetry, replace $(x,y)$ with $(-x,-y)$, we have $9(-x)^2+4(-y)^2=36$ which is the same as the original equation, thus it is symmetric with respect to the origin.
