A) \[(a,\ b)\]
B) \[(b,\ a)\]
C) \[\left( \frac{a}{2},\ \frac{b}{2} \right)\]
D) \[\left( \frac{b}{2},\ -\frac{a}{2} \right)\]
Correct Answer: C
Solution :
Let the equation of circle be \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]. Now on passing through the points, we get three equations. \[c=0\] ?.(i) \[{{a}^{2}}+2ga+c=0\] ?.(ii) \[{{b}^{2}}+2fb+c=0\] ?.(iii) On solving them, we get \[g=-\frac{a}{2},\ f=-\frac{b}{2}\] Hence the centre is\[\left( \frac{a}{2},\ \frac{b}{2} \right)\].
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