The equation of the radical axis of the circles $x^2+y^2+4x+6y+7=0$ and $4x^2+4y^2+8x+12y-9=0$ is:

The radical centre of the circles $x^2+y^2+2x+3y+1=0$,$x^2+y^2+x-y+3=0$,and $x^2+y^2-3x+2y+5=0$ is

The equation of the circle which passes through the origin and cuts orthogonally each of the circles $x^2+y^2-6x+8=0$ and $x^2+y^2-2x-2y-7=0$ is

If $S = x^2 + y^2 + 2x + 17y + 4 = 0$,$S' = x^2 + y^2 + 7x + 6y + 11 = 0$,and $S'' = x^2 + y^2 - x + 22y + 3 = 0$ are three circles,then the length of the tangent from their radical center to $S = 0$ is ......... units.

If the circles $C_1: x^2+y^2+2x+4y-20=0$ and $C_2: x^2+y^2+6x-8y+9=0$ have $n$ common tangents and the length of the tangent drawn from the centre of similitude to the circle $C_2$ is $l$,then $\frac{l}{n^2} =$

If $y = 2x$ is a chord of the circle $x^2 + y^2 - 10x = 0$,then the equation of the circle of which this chord is a diameter is: