question_answer

The angle between a pair of tangents drawn from a point P to the circle \[{{x}^{2}}+{{y}^{2}}+8x-10y+30\,{{\sin }^{2}}\alpha 0+34\,{{\cos }^{2}}\alpha =0\] is \[2\alpha \]. The equation of the locus of the point P is:

A)  \[{{x}^{2}}+{{y}^{2}}+8x-10y+40=0\]

B)  \[{{x}^{2}}+{{y}^{2}}+8x-10y+30=0\]

C)  \[{{x}^{2}}+{{y}^{2}}+8x-10y-40=0\]

D)  \[{{x}^{2}}+{{y}^{2}}+8x-10y-30=0\]

E)  None of these