Answer
For $y^2 - x^2 = -6$, it has graphs that are symmetric with respect to the $x$-axis, the $y$-axis and as well as the origin.
Work Step by Step
Appendix D - 36 (Solution)
In $y^2 - x^2 = -6$,
a) To test for symmetry w.r.t the $x$-axis
replace $y$ with $-y$, we have
$(-y)^2 - x^2 = -6$
$y^2 - x^2 = -6$
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
$y^2 - (-x)^2 = -6$
$y^2 - x^2 = -6$
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
$(-y)^2 - (-x)^2 = -6$
$y^2 - x^2 = -6$
which the result is the same as the original equation, therefore, it is symmetric with respect to the origin