If the circle $S=0$ intersect the three circle

$$ \begin{aligned} & S_1 \equiv x^2+y^2+4 x-7=0 \\ & S_2 \equiv x^2+y^2+y=0 \text { and } S_3 \equiv x^2+y^2+\frac{3}{2} x+\frac{5}{2} y-\frac{9}{2}=0 \end{aligned} $$

orthogonally, then radical axis of $S=0$ and $S_1=0$ is

If a tangent of the circle $x^2+y^2+2 x+2 y+1=0$ is radical axis of the circles $x^2+y^2+2 g x+2 f y+c=0$ and $2 x^2+2 y^2+3 x+8 y+2 c=0$, then

If the length of the chord $2 x+3 y+k=0$ of the circle $x^2+y^2-2 x+4 y-11=0$ is $2 \sqrt{3}$, then the sum of all possible values of $k$ is

The power of a point $(2,-1)$ with respect to a circle $C$ of radius 4 is 9 . The centre of the circle $C$ lies on the lines $x+y=0$ and in the 2nd quadrant. If ( $\alpha, \beta$ ) is the centre of the circle $C$ then $\beta-\alpha=$