The circle $x^2 + y^2 + 6y = 0$ touches which of the following?

Let the circle $S$ which is concentric with the circle $x^2+y^2-2x+ky+4=0$ pass through the point $(3,-2)$. If one of the diameters of $S$ lies along the line $3x-2y+4=0$,then the radius of the circle $S$ is

The equation of the circle whose end points of a diameter are the centres of the circles $x^{2}+y^{2}+2x-4y+1=0$ and $x^{2}+y^{2}-8x+6y+17=0$ is

If $P_1, P_2, P_3$ are the perimeters of the three circles $x^2+y^2+8x-6y=0$,$4x^2+4y^2-4x-12y-186=0$,and $x^2+y^2-6x+6y-9=0$ respectively,then

Let the circle $S: 36 x^{2}+36 y^{2}-108 x+120 y+C=0$ be such that it neither intersects nor touches the coordinate axes. If the point of intersection of the lines $x-2 y=4$ and $2 x-y=5$ lies inside the circle $S$,then :

If the line $3x - 2y + 6 = 0$ meets the $X$-axis and $Y$-axis at points $A$ and $B$ respectively,then the equation of the circle with radius $AB$ and center at $A$ is