Find the Standard Equation of a Sphere That Has Diameter $( 3 , - 2,4 ) , ( 7,12,4 )$

Multiple Choice

Find the standard equation of a sphere that has diameter with the end points given below. $( 3 , - 2,4 ) , ( 7,12,4 )$

A) $( x - 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 53$
B) $( x - 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 9$
C) $( x + 5 ) ^ { 2 } + ( y - 5 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 53$
D) $( x - 5 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z + 4 ) ^ { 2 } = 53$
E) $( x - 5 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 4 ) ^ { 2 } = 53$