Find the locus of the point of intersection of two tangents to the hyperbola `x^(2)/a^(2)-y^(2)/b^(2)=1`. which makes an angle `alpha` with one another.

Answer

`(x^(2)+y^2-a^(2)+b^(2))^(2)=(4a^(2)y^(2)-4b^(2)x^(2)+4a^(2)b^(2)) cot^(2) alpha`