If the circles of same radius $a$ and centers at $(2, 3)$ and $(5, 6)$ cut orthogonally,then $a =$

If the radical axis of the circles $x^2+y^2+2gx+2fy+c=0$ and $2x^2+2y^2+3x+8y+2c=0$ touches the circle $x^2+y^2+2x+2y+1=0$,then

The equation of the circle passing through the points of intersection of the circles $x^2+y^2+6x+4y-12=0$ and $x^2+y^2-4x-6y-12=0$ and having radius $\sqrt{13}$ is

If a diameter of the circle $x^2+y^2-4x+6y-12=0$ is a chord of a circle $S$ whose centre is at $(-3, 2)$,then the radius of $S$ is

If the straight line $x \cos \alpha + y \sin \alpha = P$ intersects the circle $x^2 + y^2 = a^2$ at $A$ and $B$,then the equation of the circle with diameter $\overline{AB}$ is

If the angle between the circles $x^2+y^2-2x+ky+1=0$ and $x^2+y^2-kx-2y+1=0$ is $\cos^{-1}(\frac{1}{4})$ and $k < 0$,then the point which lies on the radical axis of the given circles is