   Chapter 12.1, Problem 19E

Chapter
Section
Textbook Problem

# Show that the equation represents a sphere, and find its center and radius.2x2 + 2y2 + 2z2 = 8x − 24z + 1

To determine

To show: The equation 2x2+2y2+2z2=8x24z+1 as an equation of a sphere and to 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 2x2+2y2+2z2=8x24z+1 as follows.

2(x24x+2222)+2(y2)+2(z2+12z+6262)=12(x24x+22)+2y2+2(z2+12z+62)+(872)=

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