The radical axis of the pair of circles $x^2 + y^2 = 144$ and $x^2 + y^2 - 15x + 12y = 0$ is

If the angle between the circles $x^2+y^2-4x-6y+k=0$ and $x^2+y^2+8x-4y+11=0$ is $\frac{\pi}{3}$,then a value of $k$ is

If the circle $S=0$ cuts the circles $x^2+y^2-2x+6y=0$,$x^2+y^2-4x-2y+6=0$,and $x^2+y^2-12x+2y+3=0$ orthogonally,then the equation of the tangent at $(0,3)$ on $S=0$ is

The angle of intersection of the circles $x^2 + y^2 - x + y - 8 = 0$ and $x^2 + y^2 + 2x + 2y - 11 = 0$ is

Find the equation of a circle with radius $5$ units and touching the circle $x^2+y^2-2x-4y-20=0$ at the point $(5,5)$.

Let the circle $S \equiv x^2+y^2+2gx+2fy+c=0$ cut the circles $x^2+y^2-2x+2y-2=0$ and $x^2+y^2+4x-6y+9=0$ orthogonally. If the centre of the circle $S=0$ lies on the line $2x+3y-2=0$,then $2g+f=$