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Question

The equation of the sphere one of whose diameter has end points (1,2,4) and (3,0,2) is

A
x2+y2+z2+4x+6y+8z+11=0
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B
x2+y2+z2+4x+4y+8z11=0
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C
x2+y2+z24x2y6z+11=0
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D
x2+y2+z24x2y+6z11=0
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Solution

The correct option is C x2+y2+z24x2y6z+11=0
End point of diameter of sphere are (1,2,4) and (3,0,2).
So centre of sphere is (2,1,3) and radius is =12(13)2+(20)2+(42)2=3
Hence, equation of required sphere is
(x2)2+(y1)2+(z3)2=3
x2+y2+z24x2y6y+11=0

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