If $P\left(\frac{\pi}{4}\right), Q\left(\frac{\pi}{3}\right)$ are two points on the circle $x^2+y^2-2 x-2 y-1=0$, then the slope of the tangent to this circle which is parallel to the chord $P Q$ is

The power of a point $(2,0)$ with respect to a circle $S$ is -4 and the length of the tangent drawn from the point $(1,1)$ to $S$ is 2 . If the circle $S$ passes through the point $(-1,-1)$, then the radius of the circle $S$ is

The pole of the line $x-5 y-7=0$ with respect to the circle $S \equiv x^2+y^2-2 x+4 y+1=0$ is $P(a, b)$. If $C$ is the centre of the circle $S=0$, then $P C=$

The equation of the pair of transverse common tangents drawn to the circles $x^2+y^2+2 x+2 y+1=0$ and $x^2+y^2-2 x-2 y+1=0$ is