The circles $x^2+y^2-2x-4y-4=0$ and $x^2+y^2+2x+4y-11=0$:

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

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

The lines represented by $5x^2-xy-5x+y=0$ are normals to a circle $S=0$. If this circle touches the circle $S^{\prime} \equiv x^2+y^2-2x+2y-7=0$ externally,then the equation of the chord of contact of the centre of $S^{\prime}=0$ with respect to $S=0$ is

If the point of contact of the circles $x^2+y^2-6x-4y+9=0$ and $x^2+y^2+2x+2y-7=0$ is $(\alpha, \beta)$, then $7\beta=$ (in $\alpha$)

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