The angle between a pair of tangents drawn from a point \( P \) to the curve \( x^{2}+y^{2}+4 x-...

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The angle between a pair of tangents drawn from a point \( P \) to the curve \( x^{2}+y^{2}+4 x-6 y+9 \sin ^{2} \) \( \alpha+13 \cos ^{2} \alpha=0 \) is \( 2 \alpha \). The locus of \( P \) is
(a) \( x^{2}+y^{2}+4 x-6 y+4=0 \)
(b) \( x^{2}+y^{2}+4 x-6 y-9=0 \)
(c) \( x^{2}+y^{2}+4 x-6 y-4=0 \)
(d) \( x^{2}+y^{2}+4 x-6 y+9=0 \)
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