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Chapter 9: Q. 71 (page 622)

In Problems 71鈥�76, find the radius and center of each sphere.
x2+y2+z2+2x-2y=2

Short Answer

Expert verified

The radius and center of the sphere is

(-1,1,0)and2.

Step by step solution

01

Step 1. Given

given equation of the sphere:

x2+y2+z2+2x-2y=2

02

Step 2. Calculation

By applying the standard equation of sphere we get:

r2=(x-x0)2+(y-y0)2+(z-z0)2x2+y2+z2+2x-2y=2(x2+2x)+(y2-2y)+z2=2(x2+2x+1)+(y2-2y+1)+z2=2+1+1(x+1)2+(y-1)2+z2=4thereforecenteris(-1,1,0)andradiusis2

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