Find the center and radius of the sphere.
$$x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 16 x + 6 y + 6 z + 18 = 0$$
A) center: $( - 8,3,3 )$; radius: 8
B) center: $( 8 , - 3 , - 3 )$; radius: 8
C) center: $( 8,3,3 )$; radius: 8
D) center: $( - 8,3,3 )$; radius: 64
E) center: $( 8 , - 3 , - 3 )$; radius: 64

Question

Quizplus · Accepted Answer

To find the center and radius, complete the square for each variable. The equation becomes $(x-8)^2 + (y+3)^2 + (z+3)^2 = 64$, indicating the center is $(8, -3, -3)$ and the radius is $\sqrt{64} = 8$.

Find the Center and Radius of the Sphere x2+y2+z2−16x+6y+6z+18=0x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 16 x + 6 y + 6 z + 18 = 0x2+y2+z2−16x+6y+6z+18=0

Find the Center and Radius of the Sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 16 x + 6 y + 6 z + 18 = 0$