If $a x^2-x y-3 y^2-5 x+20 y+c=0$ represents a pair of lines passing through the point $(2,3)$, then $a-c=$

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