The radius of the circle $x^2 + y^2 + 4x + 6y + 13 = 0$ is

Four distinct points $(2k, 3k), (1, 0), (0, 1)$ and $(0, 0)$ lie on a circle for

The equation of the circle whose centre is $(1, -3)$ and which touches the line $2x - y - 4 = 0$ is

Find the equation of the circle with centre $\left(\frac{1}{2}, \frac{1}{4}\right)$ and radius $\frac{1}{12}$.

$A$ circle has its centre in the first quadrant and passes through $(2,3)$. If this circle makes intercepts of length $3$ and $4$ respectively on $x=2$ and $y=3$,its equation is

If two diameters of a circle of circumference $10 \pi$ lie along the lines $2x + 3y + 1 = 0$ and $3x - y - 4 = 0$,then the equation of the circle is