Find the equation of the chord of contact of the tangents drawn from the point $(2, -3)$ to the circle $x^2 + y^2 + 4x - 6y - 12 = 0$.

The area (in sq. units) of the triangle formed by the two tangents drawn from the external point $O(0,0)$ to the circle $x^2+y^2-2gx-2hy+h^2=0$ and their chord of contact is

$A$ circle $C_1$ of unit radius lies in the first quadrant and touches both coordinate axes. The radius of another circle that touches both coordinate axes and intersects $C_1$ such that the common chord is of maximum length is:

The length of the common chord of the two circles $x^2+y^2-4y=0$ and $x^2+y^2-8x-4y+11=0$ is

The length of the common chord of the circles $(x - a)^2 + (y - b)^2 = c^2$ and $(x - b)^2 + (y - a)^2 = c^2$ is

If the circles $x^{2}+y^{2}-2x-2y-7=0$ and $x^{2}+y^{2}+4x+2y+k=0$ cut orthogonally,then the length of the common chord of the circles is