A) \[{{y}^{2}}+6x=0\]
B) \[{{y}^{2}}+6x=13\]
C) \[{{y}^{2}}+6x=10\]
D) \[{{x}^{2}}+6y=13\]
Correct Answer: B
Solution :
Let centre of circle be\[C(-g,\,\,-f)\], then equation of circle passing through origin be \[{{x}^{2}}+{{y}^{2}}+2gx+2fy=0\] \[\therefore \]Distance,\[d=|-g-3|\,\,=g+3\] In\[\Delta ABC,\,\,{{(BC)}^{2}}=A{{C}^{2}}+B{{A}^{2}}\] \[\Rightarrow \] \[{{g}^{2}}+{{f}^{2}}={{(g+3)}^{2}}+{{2}^{2}}\] \[\Rightarrow \] \[{{g}^{2}}+{{f}^{2}}={{g}^{2}}+6g+9+4\] \[\Rightarrow \] \[{{f}^{2}}=6g+13\] Hence, required locus is\[{{y}^{2}}+6x=13\]You need to login to perform this action.
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