Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 12 - Vectors and the Geometry of Space - 12.1 Exercises - Page 815: 29

Answer

A circle of radius 2 and center (0, 0, -1), contained in the plane z = -1, which is parallel to the xy-plane and 1 unit below it.

Work Step by Step

$x^{2} + y^{2} = 4$ would represent a circle of radius 2 and center (0, 0) in the two-dimensional xy-plane. In three dimensions, that equation alone would represent an infinitely tall cylinder. However, when combining it with $z = -1$, we get the usual circle but now contained in the plane $z = -1$, which is 1 unit below the xy-plane and parallel to it. The center of this circle would be at (0, 0, -1)
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