Answer
$(\pm1,0), (0,\pm2)$,
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 $x^2=1\longrightarrow (\pm1,0)$, for y-intercept(s), let $x=0$, we have $y^2=4\longrightarrow (0,\pm2)$,
Step 2. To test for x-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $4(x)^2+(-y)^2=4$ 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 $4(-x)^2+(y)^2=4$ 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 $4(-x)^2+(-y)^2=4$ which is the same as the original equation, thus it is symmetric with respect to the origin.
