A) \[\left( \frac{1}{2},\,1,\,2 \right)\]
B) \[\left( -\frac{1}{2},\,1,\,2 \right)\]
C) \[\left( \frac{1}{2},\,1,-\,2 \right)\]
D) \[\left( 1,\frac{1}{2},\,2 \right)\]
Correct Answer: A
Solution :
Let the equation of sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2ux+2vy+2wz+d=0\] \[\because \] It passes through origin (0, 0, 0), \ \[d=0\] Also, it passes through (0, 2, 0) \ \[4+4v=0\Rightarrow v=-1\] Also, it passes through (1, 0, 0) \ \[1+2u=0\Rightarrow u=-1/2\] And it passes through (0, 0, 4) \ \[16+8w\Rightarrow w=-2\] \ Centre \[(-u,\,-v,\,-w)=\left( \frac{1}{2},\,1,\,2 \right)\].
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