Find the standard form of the equation of the sphere with the given characteristics. Center: (-6,-6,6);radius 2
A) $( x - 6 ) ^ { 2 } - ( y - 6 ) ^ { 2 } - ( z + 6 ) ^ { 2 } = 4$
B) $( x - 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } + ( z + 6 ) ^ { 2 } = 4$
C) $( x + 6 ) ^ { 2 } + ( y + 6 ) ^ { 2 } + ( z - 6 ) ^ { 2 } = 4$
D) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$
E) $( x + 6 ) ^ { 2 } - ( y + 6 ) ^ { 2 } - ( z - 6 ) ^ { 2 } = 4$

Question

Quizplus · Accepted Answer

The standard form of the equation of a sphere with center $(h, k, l)$ and radius $r$ is $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$. For a center at $(-6, -6, 6)$ and radius $2$, the equation becomes $(x + 6)^2 + (y + 6)^2 + (z - 6)^2 = 2^2$, which matches option C.

Find the Standard Form of the Equation of the Sphere (x−6)2−(y−6)2−(z+6)2=4( x - 6 ) ^ { 2 } - ( y - 6 ) ^ { 2 } - ( z + 6 ) ^ { 2 } = 4(x−6)2−(y−6)2−(z+6)2=4

Find the Standard Form of the Equation of the Sphere $( x - 6 ) ^ { 2 } - ( y - 6 ) ^ { 2 } - ( z + 6 ) ^ { 2 } = 4$