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 619: 39


$$r^2=\sec (2\theta).$$

Work Step by Step

We have $$x^2-y^2=1\Longrightarrow r^2\cos^2\theta -r^2\sin^2\theta=1\\ \Longrightarrow r^2(\cos^2\theta -\sin^2\theta)=1\\ \Longrightarrow r^2\cos(2\theta )=1. $$ Hence, the polar equation of the hyperbola is $$r^2=\sec (2\theta).$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.