If $A=(0,-2)$ and $B$ is any point on the circle $x^2+y^2-2x-2y+1=0$,then the maximum value of $(AB)^2$ is

The absolute difference between the squares of the radii of the two circles passing through the point $(-9, 4)$ and touching the lines $x+y=3$ and $x-y=3$ is equal to . . . . . . .

If a circle $C$ passing through $(4, 0)$ touches the circle $x^2 + y^2 + 4x - 6y - 12 = 0$ externally at a point $(1, -1),$ then the radius of the circle $C$ is

Let $C$ be a circle having centre in the first quadrant and touching the $x$-axis at a distance of $3$ units from the origin. If the circle $C$ has an intercept of length $6\sqrt{3}$ on the $y$-axis, then the length of the chord of the circle on the line $x - y = 3$ is:

If $\sin ^{-1}(a)$ is the acute angle between the curves $x^2+y^2=4x$ and $x^2+y^2=8$ at the point $(2,2)$,then $a$ is equal to

The number of common tangents to the circles $x^{2}+y^{2}-y=0$ and $x^{2}+y^{2}+y=0$ is