Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.6 Parametric Equations, Graphs, and Applications - 8.6 Exercises - Page 400: 52

$r = a~\theta$ $r^2 = x^2+y^2$ This is a parametric representation: $x = a~\theta~cos~\theta$ $y = a~\theta~sin~\theta$ where $-\infty \lt \theta \lt \infty$

$r^2 = x^2+y^2$ $r^2 = (a\theta~cos~\theta)^2+(a\theta~sin~\theta)^2$ $r^2 = a^2\theta^2~cos^2~\theta+a^2\theta^2~sin^2~\theta$ $r^2 = a^2\theta^2~(cos^2~\theta+~sin^2~\theta)$ $r^2 = a^2\theta^2~(1)$ $r^2 = a^2\theta^2$ $r = a~\theta$