$A$ 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

If the equation of the circle passing through the points $(-1,0),(-1,1),(1,1)$ is $a x^2+a y^2+2 g x+2 f y-2=0$, then $a=$

For the circle $x-2=5 \cos \theta, y+1=5 \sin \theta$, where $\theta$ is the perimeter, the line $x=1+\frac{r}{2}, y=-2+\frac{\sqrt{3}}{2} r$ where $r$ is the perimeter, is a

If $x-2 y=0$ is a tangent drawn at a point $P$ on the circle $x^2+y^2-6 x+2 y+c=0$, then the distance of the point $(6,3)$ from $P$ is