Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.1 Three-Dimensional Coordinate Systems - 12.1 Exercises - Page 837: 32

Answer

In 3D $x^2+y^2=4$ is a $\bf cylinder$ of radius $2$ centered on the $\bf z-axis$ extending indefinitely in the $z$ direction.

Work Step by Step

$x^2+y^2=4$ reminds us of the formula for a circle in 2D: $(x-h)^2+(y-k)^2=r^2$ where $(h,k)$ is the center and the radius is $r$ Since $h=k=0$ the center is $(0,0)$ and the radius is $r=\sqrt4 = 2$ So in 3D $x^2+y^2=4$ is a $\bf cylinder$ of radius $2$ centered on the $\bf z-axis$ extending indefinitely in the $z$ direction.
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