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

Let $\alpha, \beta$ be the roots of $x^2+5x+6=0$ and $\gamma, \delta$ be the roots of $y^2+6y+7=0$. Then the equation of the circle with $(\alpha, \gamma)$ and $(\beta, \delta)$ as the extremities of a diameter is

The equation of the circle with center at $(2, -3)$ and circumference $10 \pi$ units is

The centre of the circle $r^2-4r(\cos \theta+\sin \theta)-4=0$ in Cartesian coordinates is

$A$ circle passes through the point $(1, -2)$ and touches the $x$-axis at $(3, 0)$. Through which of the following points does it also pass?

Find the equation of the circle with center $(3, 1)$ and touching the line $8x - 15y + 25 = 0$.