Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises - Page 618: 19

$ r= \tan \theta \sec \theta $

Given $$ y=x^2$$ Since $ y=r\sin\theta,\ \ x= r\cos\theta,\ \ r^2=x^2+y^2 $, then \begin{align*} y&=x^2\\ r\sin \theta&=r^2 \cos^2\theta \\ \sin \theta&=r \cos^2\theta\\ \end{align*} Hence $$ r= \tan \theta \sec \theta $$