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Question

The equation of sphere through the points (0,0,0), (a,b,c),(a,b,c) and (a,b,c); a,b,c0

A

x2+y2+z2a2+b2+c2=xa+yb+zc

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B

x2+y2+z2a2+b2+c2=xa+ybzc

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C

x2+y2+z2a2+b2+c2=xayb+zc

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D

x2+y2+z2a2+b2+c2=xa+yb+zc

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Solution

The correct option is A

x2+y2+z2a2+b2+c2=xa+yb+zc


Equation of sphere passing through (0,0,0) is given by,
x2+y2+z2+ux+vy+wz=0
Given it also passes through (a,b,c),(a,b,c) and (a,b,c)
a2+b2+c2ua+vb+wc=0....(1)
a2+b2+c2+uavb+wc=0....(2)
a2+b2+c2+ua+vbwc=0....(3)
Solving (1),(2) and (3), we get
u=a2+b2+c2a,v=a2+b2+c2b,w=a2+b2+c2c
Therefore, equation of required sphere is
x2+y2+z2a2+b2+c2=xa+yb+zc

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