The radical axis of the circles $$S_1: x^2+y^2-4 x+6 y-10=0$$ and $$S_2 : x^2+y^2+2 x-6 y+2=0$$, cut the circle $$S_1$$ in

The locus of a point, which is at a distance of 4 units from $$(3,-2)$$ in $$x y$$-plane is

Find the equation of the circle which passes through origin and cuts off the intercepts $$-$$2 and 3 over the $$X$$ and $$Y$$-axes respectively.

The angle between the pair of tangents drawn from $$(1,1)$$ to the circle $$x^2+y^2+4 x+4 y-1=0$$ is