Answer
The equation in the example is symmetric with respect to the origin.
Work Step by Step
To verify that the equation is symmetric with respect to the origin, we will substitute $y=-y$ and $x=-x$ in the above equation. If after putting $y=-y$ and $x=-x$, the resultant equation is the same as the given equation, then the equation is symmetric with respect to the origin.
$\begin{align}
& {{y}^{2}}={{x}^{2}}+8 \\
& {{\left( -y \right)}^{2}}={{\left( -x \right)}^{2}}+8\text{ } \\
& {{y}^{2}}={{x}^{2}}+8
\end{align}$
Since the resultant equation is the same as the given equation, the equation is symmetric with respect to the origin.
