The correct option is D x2+y2+4x−6y+9=0
Let P(x1,y1) be a point in the locus
Radius of S≡x2+y2+4x−6y+9sin2α+13cos2α=0
r=√(−2)2+(−3)2−9sin2α−13cos2α=√13(1−cos2α)−9sin2α=2sinα
Length of the tangent from P(x1,y1) to S = 0 is √S11=√x21+y21+4x1−6y1+9sin2α+13cos2α
Since 2α is the angle between the tangent drawn from P to S = 0
we have tanα=r√s11⇒S11.tan2α=r2⇒(x21+y21+4x1−6y1+9sin2α+13cos2α)tan2α=4sin2α⇒(x21+y21+4x1−6y1+9+4cos2α)sin2αcos2α=4sin2α⇒(x21+y21+4x1−6y1+9)sec2α=0⇒x21+y21+4x1−6y1+9=0Locus of (x1,y1) is x2+y2+4x−6y+9=0