Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 12 - Vectors and the Geometry of Space - 12.1 Exercises - Page 814: 13

Answer

$(x-3)^2+(y-8)^2+(z-1)^2=30$

Work Step by Step

Since the sphere is centered at $(3,8,1)$ and passes through $(4,3,-1)$, we know the radius is the distance between these two points. Using the distance formula, we get $$r=\sqrt{(3-4)^2+(8-3)^2+(1+1)^2} \\=\sqrt{(-1)^2+(5)^2+(2)^2} \\=\sqrt{1+25+4}\\=\sqrt{30}.$$ Hence we have a sphere centered at $(3,8,1)$ and with radius $r=\sqrt{30}$. Thus the equation of the sphere is $$(x-3)^2+(y-8)^2+(z-1)^2=30$$
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