Find the standard form of the equation of the sphere with the given characteristics.
Center: (-4,1,-7);radius 9
A) $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 81$
B) $( x + 4 ) ^ { 2 } - ( y - 1 ) ^ { 2 } - ( z + 7 ) ^ { 2 } = 81$
C) $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } - ( z + 7 ) ^ { 2 } = 81$
D) $( x + 4 ) ^ { 2 } - ( y - 1 ) ^ { 2 } + ( z + 7 ) ^ { 2 } = 81$
E) $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z + 7 ) ^ { 2 } = 81$

Question

Find the standard form of the equation of the sphere with the given characteristics. 
Center: (-4,1,-7);radius 9
A) $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 81$
B) $( x + 4 ) ^ { 2 } - ( y - 1 ) ^ { 2 } - ( z + 7 ) ^ { 2 } = 81$
C) $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } - ( z + 7 ) ^ { 2 } = 81$
D) $( x + 4 ) ^ { 2 } - ( y - 1 ) ^ { 2 } + ( z + 7 ) ^ { 2 } = 81$
E) $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z + 7 ) ^ { 2 } = 81$

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 $(-4, 1, -7)$ and radius $9$, the equation becomes $(x + 4)^2 + (y - 1)^2 + (z + 7)^2 = 81$, matching choice E.

Find the Standard Form of the Equation of the Sphere (x−4)2+(y+1)2+(z−7)2=81( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 81(x−4)2+(y+1)2+(z−7)2=81

Find the Standard Form of the Equation of the Sphere $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 81$