The locus of the point of Interection of two tangents to the hyperbola `x^(2)/a^(2)-y^(2)/b^(2)=1` which a make an angle `60^@` with one another is

Options

A. `(x^(2)+y^(2) -a^(2)+b^(2))^(2)=12(a^(2)y^(2)-b^(2)x^(2)+a^(2)b^(2))`
B. `(x^(2)+y^(2) -a^(2)+b^(2))^(2)=4(a^(2)y^(2)-b^(2)x^(2)+a^(2)b^(2))`
C. `3(x^(2)+y^(2) -a^(2)+b^(2))^(2)=4(a^(2)y^(2)-b^(2)x^(2)+a^(2)b^(2))`
D. `x^(2)+y^(2)=a^(2)-b^(2^(2)`

Answer

C