If the angle between the pair of tangents drawn to the circle $x^2+y^2-2 x+4 y+3=0$ from the point $(6,-5)$ is $\theta$, then $\cot \theta=$

If the angle between the circles $x^2+y^2-4 x-6 y+k=0$ and $x^2+y^2+8 x-4 y+11=0$ is $\frac{\pi}{2}$, then the value of $k$ is

The radius of a circle touching all the four circles $(x \pm \lambda)^2+(y \pm \lambda)^2=\lambda^2$ is

If the radical centre of the given three circles $x^2+y^2=1, x^2+y^2-2 x-3=0$ and $x^2+y^2-2 y-3=0$ is $C(\alpha, \beta)$ and $r$ is the sum of the radii of the given circles, then the circle with $C(\alpha, \beta)$ as centre and $r$ as radius is