Find the standard equation of the sphere with center $C$ and radius $r$.
$$C ( 4 , - 1,5 ) ; r = 8$$
A) $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z + 5 ) ^ { 2 } = 64$
B) $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z + 5 ) ^ { 2 } = 8$
C) $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 8$
D) $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 64$

Question

Quizplus · Accepted Answer

The standard equation of a sphere with center $(h,k,l)$ and radius $r$ is given by $(x-h)^2+(y-k)^2+(z-l)^2=r^2$. Using the given information, we get $(x-4)^2+(y+1)^2+(z-5)^2=8^2$, which simplifies to $(x-4)^2+(y+1)^2+(z-5)^2=64$. Thus, the correct choice is D.

Find the Standard Equation of the Sphere with Center CCC And Radius

Find the Standard Equation of the Sphere with Center $C$ And Radius