Suppose $C_1$ and $C_2$ are two circles having no common points, then

The locus of the centre of the circle touching the $X$-axis and passing through the point $(-1,1)$ is

The centres of all circles passing through the points of intersection of the circles $x^2+y^2+2 x-2 y+1=0$ and $x^2+y^2-2 x+2 y-2=0$ and having radius $\sqrt{14}$ lie on the curve

$A$ circle $S$ given by $x^2+y^2-14 x+6 y+33=0$ cuts the $X$-axis at $A$ and $B(O B>O A)$. $C$ is mid-point of $A B . L$ is a line through $C$ and having slope ( -1 ). If $L$ is the diameter of a circle $S^{\prime}$ and also the radical axis of the circles $S$ and $S^{\prime}$, then the equation of the circle $S^{\prime}$ is