Change to polar coordinates the equation $\;$ $x^2 + y^2 = a^2$.
The relation between Cartesian coordinates $\left(x, y\right)$ and polar coordinates $\left(r, \theta\right)$ is
$x = r \cos \theta$, $\;\;$ $y = r \sin \theta$
$\begin{aligned}
\therefore \; x^2 + y^2 = a^2 & \implies r^2 \cos^2 \theta + r^2 \sin^2 \theta = a^2 \\\\
& i.e. \;\; r^2 \left(\cos^2 \theta + \sin^2 \theta\right) = a^2 \\\\
& i.e. \;\; r^2 = a^2 \\\\
& i.e. \;\; r = a
\end{aligned}$
$\therefore \;$ The polar form of the given Cartesian equation $\;$ $x^2 + y^2 = a^2$ $\;$ is $\;$ $r = a$.