For the circle $x^2 + y^2 + 3x + 3y = 0$,which of the following relations is true?

If the radius of a circle $x^{2}+y^{2}-4x+6y-k=0$ is $5$,then $k=$

If the equation of the circle having its centre in the second quadrant touches the coordinate axes and also the line $\frac{x}{5}+\frac{y}{12}=1$ is $x^2+y^2+2 \lambda x-2 \lambda y+\lambda^2=0$,then $\lambda=$

Find the equation of a circle with radius $4$ that touches the $x$-axis at a distance of $-3$ from the origin.

Find the equation of the circle passing through $(1, -2)$ and touching the $x$-axis at $(3, 0)$.

$A$ line is drawn through a fixed point $P(\alpha, \beta)$ to cut the circle $x^2 + y^2 = r^2$ at $A$ and $B$. Then $PA \cdot PB$ is equal to