Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

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


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

Work Step by Step

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