## Precalculus (10th Edition)

We are given the equation: $y^2=9+x^2$ Test the equation for symmetry with respect to the $x$-axis: replace $y$ with $-y$ and simplify: $(-y)^2=9+x^2$ $y^2=9+x^2$ We got an equivalent equation; therefore the equation is symmetric with respect to the $x$-axis. Test the equation for symmetry with respect to the $y$-axis: replace $x$ with $-x$ and simplify: $y^2=9+(-x)^2$ $y^2=9+x^2$ We got an equivalent equation; therefore the equation is symmetric with respect to the $y$-axis. Test the equation for symmetry with respect to the origin: replace $x$ by $-x$ and $y$ by $-y$ and simplify: $(-y)^2=9+(-x)^2$ $y^2=9+x^2$ We got an equivalent equation; therefore the equation is symmetric with respect to the origin. Therefore the given statement is TRUE.