Let the given points be $A(a, b)$ and $B(-a,-b)$. The equation of line passing through the points A and $B$ is
$$
\begin{array}{ll}
y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right) \\
\Rightarrow \quad y-b=\frac{-b-b}{-a-a}(x-a) \\
\Rightarrow \quad y-b=\frac{2 b}{2 a}(x-a)
\end{array}
$$
$\Rightarrow \quad y-b=\frac{b}{a}(x-a)$
$\Rightarrow \quad a y-a b=b x-a b$
$$
\Rightarrow \quad b x=a y ...(i)
$$
Since, from the given points $\left(a^{2}, a b\right)$ and $(a, b)$ are satisty the Eq. (i), but ( $a^{2}$, ab) is the required answer because $(a, b)$ is already given in question.