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: 17

Answer

Center is at (1, 2, -4) and the radius is 6

Work Step by Step

$x^{2} + y^{2} + z^{2} - 2x - 4y + 8z = 15 $ $x^{2} - 2x + y^{2} - 4y + z^{2} + 8z = 15 $ $x^{2} - 2x +1 + y^{2} - 4y +4 + z^{2} + 8z + 16 = 15 + 1 + 4 + 16 $ $(x-1)^{2} + (y-2)^{2} + (z+4)^{2} = 36 $ This is indeed a sphere, the center is at (1, 2, -4) and the radius is 6
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