The slope of a common tangent to the circles $x^2+y^2-4 x-8 y+16=0$ and $x^2+y^2-6 x-16 y+64=0$ is

$x^2+y^2+2 x-6 y-6=0$ and $x^2+y^2-6 x-2 y+k=0$ are two intersecting circles and $k$ is not an integer. If $\theta$ is the angle between the two circles and $\cos \theta=\frac{-5}{24}$, then $k=$

If $(p, q)$ is the centre of the circle which cuts the three circles $x^2+y^2-2 x-4 y+4=0, x^2+y^2+2 x-4 y+1=0$ and $x^2+y^2-4 x-2 y-11=0$ orthogonally, then $p+q=$

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