Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.1 - Three-Dimensional Coordinate Systems - Exercises 12.1 - Page 696: 33


$x^{2}+y^{2}=16,\qquad z=3$

Work Step by Step

Plane: perpendicular to the z-axis $\Rightarrow$ parallel to the xy-plane ($z=0)$ Passes through a point in which $z=3 \Rightarrow$ the plane is $z=3$ . Sphere:$\qquad x^{2}+y^{2}+z^{2}=25$ Substitute z=3 into the equation for the sphere, $x^{2}+y^{2}+9=25,\qquad z=3$ $x^{2}+y^{2}=16,\qquad z=3$ (circle of radius 4 in the plane $z=3$, centered on the z-axis).
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