A) \[(-g,\,-f)\]
B) \[(g,f)\]
C) \[(-f,-g)\]
D) None of these
Correct Answer: D
Solution :
Equation of pair of tangents from (0, 0) to circle are\[S{{S}_{1}}={{T}^{2}}\]. Equation of circle through origin and chord of contact is \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c+\lambda (gx+fy+c)=0\] \[\Rightarrow \lambda =-1\] (by\[x=0,\ y=0\]) Therefore, equation is \[{{x}^{2}}+{{y}^{2}}+gx+fy=0\]. Hence circumcentre is \[\left( -\frac{g}{2},\ -\frac{f}{2} \right)\] Aliter: Required circumcentre is the mid-point of (0, 0) and \[(-g,\ -f)\] i.e., \[\left( -\frac{g}{2},\ -\frac{f}{2} \right)\].You need to login to perform this action.
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