   Chapter 12.1, Problem 18E

Chapter
Section
Textbook Problem

# Show that the equation represents a sphere, and find its center and radius.x2 + y2 + z2 + 8x − 6y + 2z + 17 = 0

To determine

To show: The equation x2+y2+z2+8x6y+2z+17=0 as an equation of a sphere and determine the center and radius of the sphere.

Explanation

Consider a sphere with center C(h,k,l) and radius r.

Formula:

Write the expression to find an equation of a sphere with center C(h,k,l) and radius r.

(xh)2+(yk)2+(zl)2=r2 (1)

Here,

(h,k,l) is the center of a sphere and

r is the radius of a sphere.

Rearrange the expression x2+y2+z2+8x6y+2z+17=0 as follows.

(x2+8x+4242)+(y26y+3232)+(z2+2z+1212)+17=0(x2+8x+42)+(y26y+32)+(z2+2z

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