Find the standard form of the equation of the sphere with the given characteristics. Endpoints of a diameter: (-7,0,0), (-3,2,4)
A) $( x + 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 36$
B) $( x + 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 18$
C) $( x - 5 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + ( z + 2 ) ^ { 2 } = 9$
D) $( x + 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 9$
E) $( x + 5 ) ^ { 2 } - ( y - 1 ) ^ { 2 } - ( z - 2 ) ^ { 2 } = 9$

Question

Quizplus · Accepted Answer

The center of the sphere is the midpoint of the diameter, which is (-5,1,2). The radius of the sphere is half the length of the diameter, which is 5. So the equation of the sphere is:$$(x + 5)^2 + (y - 1)^2 + (z - 2)^2 = 5^2 = 25$$

Find the Standard Form of the Equation of the Sphere (x+5)2+(y−1)2+(z−2)2=36( x + 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 36(x+5)2+(y−1)2+(z−2)2=36

Find the Standard Form of the Equation of the Sphere $( x + 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 36$