Calculus (3rd Edition)

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

Chapter 13 - Vector Geometry - 13.7 Cylindrical and Spherical Coordinates - Exercises - Page 700: 32


$$ r^2= \frac{2z}{3 \sin2\theta} .$$

Work Step by Step

Since $$ x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$ then $ z=3xy $ takes the form $$ z=3r^2\cos \theta \sin\theta \Longrightarrow r^2=\frac{z}{3\cos \theta \sin\theta}=\frac{2z}{3 \sin2\theta} .$$
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