A) 1
B) -1
C) 2
D) -2
Correct Answer: C
Solution :
[c] The given equation of sphere is \[a{{x}^{2}}+b{{y}^{2}}+c{{z}^{2}}-2x+4y+2z-3=0\] This equation represents a equation of sphere, if coefficient of \[{{x}^{2}},{{y}^{2}}\] and \[{{z}^{2}}\] is same. i.e., a =b =c \[\therefore \] Equation of sphere can be re-written as \[b{{x}^{2}}+b{{y}^{2}}+b{{z}^{2}}-2x+4y+2z-3=0\] \[\Rightarrow {{x}^{2}}+{{y}^{2}}+{{Z}^{2}}-\frac{2x}{b}+\frac{4y}{b}+\frac{2z}{b}-\frac{3}{b}=0\] The centre of this sphere is \[\left( \frac{1}{b},\frac{-2}{b},\frac{-1}{b} \right)\] Given that the centre of sphere is \[\left( \frac{1}{2},-1,-\frac{1}{b} \right)\] \[\frac{1}{b}=\frac{1}{2}\Rightarrow b=2\]
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