Answer
True
Work Step by Step
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.
