Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 12 - Section 12.1 - Three-Dimensional Coordinate Systems - 12.1 Exercises: 13

Answer

$(x+3)^2+(y-2)^2+(z-5)^2=4^2$ The sphere intersects the yz-plane at $(y-2)^2+(z-5)^2=4^2-3^2=7$

Work Step by Step

The equation can be found using the formula for a sphere: $(x-h)^2+(y-k)^2+(z-l)^2=r^2$ in which the point $(h,k,l)$ is the center of the sphere, and $r$ is the radius of the sphere. The intersection with the yz-plane can be determined by setting $x=0$ $(0+3)^2+(y-2)^2+(z-5)^2=4^2$ $(3)^2+(y-2)^2+(z-5)^2=4^2$ $(y-2)^2+(z-5)^2=4^2-3^2=7$
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