Calculus (3rd Edition)

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

Chapter 14 - Calculus of Vector-Valued Functions - 14.1 Vector-Valued Functions - Exercises - Page 710: 18


Circle in the vertical plane $(x=7)$ of radius $12$ centered at the $(7,0,0)$.

Work Step by Step

We put $$ x=7,\quad y=12\cos t, \quad z=12\sin t $$ hence we get $$ y^2+z^2=144\sin^2t+144\cos^2t=144.$$ Which is a circle in the vertical plane $(x=7)$ of raduis $12$ centered at the $(7,0,0)$.
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