Answer
The given equation is symmetric about the origin.
Work Step by Step
$x^{2}y^{2}+xy=1$
Test for symmetry about the $y$-axis by substituting $x$ by $-x$ and simplifying:
$(-x)^{2}y^{2}+(-x)y=1$
$x^{2}y^{2}-xy=1$
Since substituting $x$ by $-x$ does not yield an equivalent equation, the equation is not symmetric about the $y$-axis.
Test for symmetry about the $x$-axis by substituting $y$ by $-y$ and simplifying:
$x^{2}(-y)^{2}+x(-y)=1$
$x^{2}y^{2}-xy=1$
Since substituting $y$ by $-y$ does not yield an equivalent equation, the equation is not symmetric about the $x$-axis.
Test for symmetry about the origin by substituting $x$ by $-x$ and $y$ by $-y$ and simplifying:
$(-x)^{2}(-y)^{2}+(-x)(-y)=1$
$x^{2}y^{2}+xy=1$
Since substituting $x$ by $-x$ and $y$ by $-y$ yields an equivalent equation, the equation is symmetric about the origin.