The circle passing through $(1, -2)$ and touching the $x$-axis at $(3, 0)$ also passes through the point

If a circle passing through $(1, -2)$ has $x - y = 2$ and $2x + 3y = 14$ as its diameters,then the radius of the circle is

The equation of the circle passing through the origin,whose center lies in the first quadrant and which makes intercepts of length $6$ and $4$ on the $x$-axis and $y$-axis respectively,is:

$A$ circle touches both axes and its center lies in the fourth quadrant. If its radius is $1$,then its equation is:

Circles are drawn through the point $(2, 0)$ to cut an intercept of length $5$ units on the $x$-axis. If their centres lie in the first quadrant,then their equation is

Find the equation of the circle with centre $(0,2)$ and radius $2$.