Answer
The equation is symmetric about the $x$-axis, the $y$-axis and the origin.
Work Step by Step
$x^{4}y^{4}+x^{2}y^{2}=1$
Test for symmetry about the $y$-axis by substituting $x$ by $-x$ and simplifying:
$(-x)^{4}y^{4}+(-x)^{2}y^{2}=1$
$x^{4}y^{4}+x^{2}y^{2}=1$
Since substituting $x$ by $-x$ yields an equivalent equation, the equation is symmetric about the $y$-axis.
Test for symmetry about the $x$-axis by substituting $y$ by $-y$ and simplifying:
$x^{4}(-y)^{4}+x^{2}(-y)^{2}=1$
$x^{4}y^{4}+x^{2}y^{2}=1$
Since substituting $y$ by $-y$ yields an equivalent equation, the equation is symmetric about the $x$-axis.
Since this equation is symmetric about both the $x$-axis and $y$-axis, we can also say the equation is symmetric about the origin.
