angle betw pair of tangents drawn on P to the circle x^2+y^2+4x-6y+9 sin^2⁡ α+13 cos^2⁡ α=0 is 2α.

The angle between a pair of tangents drawn from a point P to the circle, x^2+y^2+4x-6y+9 sin^2⁡〖α+13 cos^2⁡〖α=0〗 〗 is 2α. Then the locus of P is
(a) x^2+y^2+4x-6y+4=0
(b) x^2+y^2+4x-6y-9=0
(c) x^2+y^2+4x-6y-4=0
(d) x^2+y^2+4x-6y+9=0
Ans: d
Sol.
Let P(h,k).
Radius of the given circle =2 sin⁡〖α,〗 centre =(-2,3)
From ∆OPA,sin⁡〖α=OA/OP=(2 sin⁡α)/OP〗⇒OP=2
or (h+2)^2+(k-3)^2=2^2
or h^2+k^2+4h-6k+9=0
∴ Locus is x^2+y^2+4x-6y+9=0

angle betw pair of tangents drawn on P to the circle x^2+y^2+4x-6y+9 sin^2⁡ α+13 cos^2⁡ α=0 is 2α.
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