Answer
For $x^2 + y^2 = 12$, it has graphs that are symmetric to the $x$-axis, the $y$-axis and as well as the origin.
Work Step by Step
In $x^2 + y^2 = 12$,
a) To test for symmetry w.r.t the $x$-axis
replace $y$ with $-y$, we have
$x^2 + (-y)^2 = 12$
$x^2 + y^2 = 12$
which the result is the same as the original equation, therefore, it is symmetric with respect to the $x$-axis
b) To test for symmetry w.r.t the $y$-axis
replace $x$ with $-x$, we have
$(-x)^2 + y^2 = 12$
$x^2 + y^2 = 12$
which the result is the same as the original equation, therefore, it is symmetric with respect to the $y$-axis
c) To test for symmetry w.r.t the origin
replace $x$ with $-x$ and $y$ with $-y$, we have
$(-x)^2 + (-y)^2 = 12$
$x^2 + y^2 = 12$
which the result is the same as the original equation, therefore, it is symmetric with respect to the origin