Let a chord $A B$ subtend an angle of $60^{\circ}$ at the centre $C(2,3)$ of a circle $S$. If the equation of $A B$ is $x+y+1=0$, then the equation of the circle $S$ is

Let 6,8 be the $X$ and $Y$-intercepts made by the circle $S \equiv x^2+y^2+2 g x+2 f y+c=0$, respectively. If $g x+f y+1=0$ is a line passing through the point $(1,-1)$, then the radius of the circle $S=0$ is

If $(3,1)$ and $(-2,4)$ are points on a circle $S$ whose centre lies on the line $x-y+1=0$, then the parametric equations of $S$ are

Let $S \equiv x^2+y^2-8 x+10 y+5=0$ be a circle. Let $P(1,1)$ and $Q(1,-1)$ be two points. Then, the point of intersection of the polar of $P$ with respect to $S=0$ and the chord with $Q$ as mid-point to $S=0$ is