Find the center and radius of the sphere for this equation x2+12x+y2-18y+z2+16z=-132

Question

Find the center and radius of the sphere for this equation

x2+12x+y2−18y+z2+16z=−132

Answer 1

An equation of the sphere with center (a,b,c) and radius r is 

 

(x-a)²+(y-b)²+(z-c)² = r².

 

Put the given equation in this form by completing the square:

 

(x²+12x) + (y²-18y) + (z²+16z) = -132

 

(x²+12x+36) + (y²-18y+81) + (z²+16z+64) = -132+36+81+64

 

(x+6)² + (y-9)² + (z+8)² = 49

 

The center is (-6, 9, -8) and the radius is 7.