A) \[\left( -\frac{1}{2},1,2 \right)\]
B) \[\left( 1,\frac{1}{2},2 \right)\]
C) \[\left( \frac{1}{2},1,2 \right)\]
D) \[\left( \frac{1}{2},1,-2 \right)\]
Correct Answer: C
Solution :
Let the equation of sphere be \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2ux+2vy+2wz+d=0\] Since, it passes through (0, 0, 0) \[\therefore \] \[d=0\] Also, it passes through (0, 2, 0), (1, 0,1), (0, 0, 4) respectively are \[4+4v=0\Rightarrow v=-1\] \[1+2u=0\Rightarrow u=-\frac{1}{2}\] and \[16+8\omega \Rightarrow \omega =-2\] \[\therefore \]centre is \[(-u,-v,-\omega )=\left( \frac{1}{2},1,2 \right)\]
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