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Chapter 10: Q 38 (page 789)

Find the center and radius of the sphere with the given equation:

x2+y2+z2-2x+6y-8z+17=0

Short Answer

Expert verified

The center is (1, -3, 4) and radius is 3.

Step by step solution

01

Given information

The given equation of a sphere is:x2+y2+z2-2x+6y-8z+17=0

02

Finding the radius and center

Converting the equation to whole square in variablesx,yandz:

x2+y2+z2-2x+1+6y+9-8z+16+17-26=0

Isolating the variables:

(x-1)2+(y+3)2+(z-4)2=32

Comparing with equation of sphere, center is at (1, -3, 4) and radius is 3.

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