Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 9 - Section 9.3 - Three-Dimensional Coordinate Geometry - 9.3 Exercises - Page 652: 17

Answer

center $(6, 1, 0)$, radius $\sqrt{37}$

Work Step by Step

$x^2+y^2+z^2=12x+2y$ $x^2-12x+y^2-2y+z^2=0$ $x^2-12x+(\frac{-12}{2})^2+y^2-2y+(\frac{-2}{2})^2+z^2=0+(\frac{-12}{2})^2+(\frac{-2}{2})^2$ $x^2-12x+36+y^2-2y+1+z^2=36+1$ $(x-6)^2+(y-1)^2+z^2=37$ This is a sphere with center $(6, 1, 0)$ and radius $\sqrt{37}$.
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