University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.1 - Three-Dimensional Coordinate Systems - Exercises - Page 600: 33

Answer

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

Work Step by Step

The plane: - is perpendicular to the z-axis $\Rightarrow$ parallel to the xy-plane ($z=0)$ - passes through in which $z=3 \Rightarrow$ the plane is $z=3$ . Substitute z=3 into the equation for the sphere,$\qquad x^{2}+y^{2}+z^{2}=25$ $x^{2}+y^{2}+9=25,\qquad z=3$ $x^{2}+y^{2}=16,\qquad z=3$ Thus, we get a circle in the plane $z=3$.
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