Find the standard form of the equation of the sphere with the given characteristics.
Endpoints of a diameter: $( - 8,4 , - 2 ) , ( - 8 , - 2,6 )$
A) $( x + 16 ) ^ { 2 } + ( x - 2 ) ^ { 2 } + ( x - 4 ) ^ { 2 } = 25$
B) $( x + 8 ) ^ { 2 } + ( x - 1 ) ^ { 2 } + ( x - 2 ) ^ { 2 } = 50$
C) $( x + 8 ) ^ { 2 } + ( x - 1 ) ^ { 2 } + ( x - 2 ) ^ { 2 } = 100$
D) $( x + 8 ) ^ { 2 } + ( x - 1 ) ^ { 2 } + ( x - 2 ) ^ { 2 } = 25$
E) $( x - 8 ) ^ { 2 } + ( x + 1 ) ^ { 2 } + ( x + 2 ) ^ { 2 } = 25$

Question

Quizplus · Accepted Answer

The center of the sphere is the midpoint of the diameter, calculated as $(-8, 1, 2)$. The radius is half the distance between the endpoints, which is 5. The equation of the sphere is $(x + 8)^2 + (y - 1)^2 + (z - 2)^2 = 25$.

Find the Standard Form of the Equation of the Sphere (−8,4,−2),(−8,−2,6)( - 8,4 , - 2 ) , ( - 8 , - 2,6 )(−8,4,−2),(−8,−2,6)

Find the Standard Form of the Equation of the Sphere $( - 8,4 , - 2 ) , ( - 8 , - 2,6 )$