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

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

Find the equation of a circle whose diameters are $2x - 3y = 5$ and $3x - 4y = 7$ and whose radius is $8$.

The equation of the circle with radius $5$ and touching the coordinate axes in the third quadrant is:

Let the circles pass through the point $(-1, 1)$ and be tangent to the $x$-axis. If $(h, k)$ are the coordinates of the center of the circle,then the set of values of $k$ is given by which interval?

If a circle passing through $(4, -2)$ is concentric with the circle $x^2 + y^2 - 2x + 4y + 20 = 0$,then find the value of $c$ for the circle $x^2 + y^2 - 2x + 4y + c = 0$.