A) \[\left( 13,\,\,\frac{33}{4} \right)\]
B) \[\left( \frac{33}{4},\,\,-13 \right)\]
C) \[\left( \frac{33}{4},\,\,13 \right)\]
D) None of these
Correct Answer: D
Solution :
Given, equation of the circles are \[{{S}_{1}}\equiv {{x}^{2}}+{{y}^{2}}-16x+60=0\] ... (i) \[{{S}_{2}}\equiv {{x}^{2}}+{{y}^{2}}-12x+27=0\] ... (ii) And \[{{S}_{3}}\equiv {{x}^{2}}+{{y}^{2}}-12y+8=0\] ... (iii) The radical axis of circles (i) and (ii) is \[{{S}_{1}}-{{S}_{2}}=0\] \[\Rightarrow \] \[({{x}^{2}}+{{y}^{2}}-16x+60)\] \[-({{x}^{2}}+{{y}^{2}}-12x+27)=0\] \[\Rightarrow \] \[-4x+33=0\] \[\Rightarrow \] \[x=\frac{33}{4}\] ? (iv) The radical axis of circles (ii) and (iii) is \[{{S}_{2}}-{{S}_{3}}=0\] \[\Rightarrow \] \[({{x}^{2}}+{{y}^{2}}-12x+27)\] \[-({{x}^{2}}+{{y}^{2}}-12y+8)=0\] \[\Rightarrow \] \[-12x+12y+19=0\] ? (v) On solving Eqs. (iv) and (v), wef get radical centre\[\left( \frac{33}{4},\,\,\frac{20}{3} \right)\].
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