Answer
$r ~\theta = a$
$r^2 = x^2+y^2$
This is a parametric representation:
$x = \frac{a~cos~\theta}{\theta}$
$y = \frac{a~sin~\theta}{\theta}$
for $\theta$ in $(-\infty, 0) \cup (0, \infty)$
Work Step by Step
$r^2 = x^2+y^2$
$r^2 = (\frac{a~cos~\theta}{\theta})^2+ (\frac{a~sin~\theta}{\theta})^2$
$r^2 = \frac{a^2~cos^2~\theta}{\theta^2}+ \frac{a^2~sin^2~\theta}{\theta^2}$
$r^2 = \frac{a^2}{\theta^2}~(cos^2~\theta+sin^2~\theta)$
$r^2 = \frac{a^2}{\theta^2}~(1)$
$r^2 = \frac{a^2}{\theta^2}$
$r = \frac{a}{\theta}$
$r ~\theta = a$
