The angle between the tangents drawn from the point $P(k, 6 k)$ to the circle $x^2+y^2+6 x-6 y+2=0$ is $2 \tan ^{-1}\left(\frac{4}{3}\right)$. If the coordinates of $P$ are integers, then $k=$

The tangents drawn from a point $(2,-1)$ touch the circle $x^2+y^2+4 x-2 y+1=0$ at the points $A$ and $B$. If $C$ is the centre of the circle, then the area (in sq. units) of the $\triangle A B C$ is

If $\theta$ is the angle between the circles $x^2+y^2-4 x+2 y-4=0$ and $x^2+y^2-2 x+4 y-11=0$ then $\sin \theta=$

If the line $x+y=2$ cuts the circle $x^2+y^2+2 x-4 y+4=0$ at two points $A$ and $B$, then the radius of the circle passing through $A, B$ and orthogonal to $x^2+y^2-2 x-4 y-4=0$ is