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

If the circle $$x^2+y^2-4 x-8 y-5=0$$ intersects the line $$3 x-4 y-m=0$$ in two distinct points, then the number of integral values of '$$m$$' is

Let $$C$$ be the circle center $$(0,0)$$ and radius 3 units. The equation of the locus of the mid-points of the chords of the circle $$c$$ that subtends an angle of $$\frac{2 \pi}{3}$$ at its centre is

The length of the common chord of the circles $$x^2+y^2+3x+5y+4=0$$ and $$x^2+y^2+5x+3y+4=0$$ is __________ units.