   Chapter 12.1, Problem 20E

Chapter
Section
Textbook Problem

# Show that the equation represents a sphere, and find its center and radius.3x2 + 3y2 + 3z2 = 10 + 6y + 12z

To determine

To show: The equation 3x2+3y2+3z2=10+6y+12z 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 3x2+3y2+3z2=10+6y+12z as follows.

3x2+3(y22y+1212)+3(z24z+2222)=103x2+3(y22y+12)+3(z24z+22)+(312

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