Find the standard equation of the sphere with center (2, 8, 4), and radius 2.
A) $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z + 4 ) ^ { 2 } = 4$
B) $( x + 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 2$
C) $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 2$
D) $( x - 2 ) ^ { 2 } + ( y + 8 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 4$
E) $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 4$

Question

Find the standard equation of the sphere with center (2, 8, 4), and radius 2. 
A) $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z + 4 ) ^ { 2 } = 4$
B) $( x + 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 2$
C) $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 2$
D) $( x - 2 ) ^ { 2 } + ( y + 8 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 4$
E) $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 4$

Quizplus · Accepted Answer

The standard equation of a sphere with center $(a,b,c)$ and radius $r$ is $(x-a)^2+(y-b)^2+(z-c)^2=r^2$. Substituting the given values, we get $(x-2)^2+(y-8)^2+(z-4)^2=2^2$, which simplifies to $(x-2)^2+(y-8)^2+(z-4)^2=4$. Therefore, the correct choice is E.

Find the Standard Equation of the Sphere with Center (2 (x−2)2+(y−8)2+(z+4)2=4( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z + 4 ) ^ { 2 } = 4(x−2)2+(y−8)2+(z+4)2=4

Find the Standard Equation of the Sphere with Center (2 $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } + ( z + 4 ) ^ { 2 } = 4$