If $(a, b)$ is the common point for the circles $x^2+y^2-4 x+4 y-1=0$ and $x^2+y^2+2 x-4 y+1=0$, then $a^2+b^2=$

The angle between the tangents drawn from the point $(2,2)$ to the circle $x^2+y^2+4 x+4 y+c=0$ is $\cos ^{-1}\left(\frac{7}{16}\right)$. If two such circles exist, then sum of the values of $c$ is

If the circle $S=x^2+y^2+2 g x+4 y+1=0$ bisects the circumference of the circle $x^2+y^2-2 x-3=0$, then the radius of circle $S=0$ is

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4 x$ is