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: 20

Answer

Circle in the vertical plane $(y=9)$ of raduis $3 $ centered at $(6,9,4)$.

Work Step by Step

We put $$ x=6+3\sin t,\quad y=9, \quad z=4+3\cos t $$ hence we get $$(x-6)^2+(z-4)^2=9\sin^2t+9\cos^2t=9.$$ Which is a circle in the vertical plane $(y=9)$ of raduis $3 $ centered at $(6,9,4)$.
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