Question

A chord \(A B\) is drawn from the point \(A(0,3)\) on the circle \(x^{2}+4 x+(y-3)^{2}=0\), and is extended to \(M\) such that \(\mathrm{AM}=2 \mathrm{AB} .\) The locus of \(\mathrm{M}\) is
(A) \(x^{2}+y^{2}-8 x-6 y+9=0\)
(B) \(x^{2}+y^{2}+8 x+6 y+9=0\)
(C) \(x^{2}+y^{2}+8 x-6 y+9=0\)
(D) \(x^{2}+y^{2}-8 x+6 y+9=0\)
Ans: (C)

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