For the two circles $x^2 + y^2 = 16$ and $x^2 + y^2 - 2y = 0$,there is/are:

The length of the diameter of a circle which touches the $x$-axis at the point $(1, 0)$ and passes through the point $(2, -3)$ is:

The equation of the circle inscribed in a square formed by the lines $x+y-2=0$,$x+y-6=0$,$x-y+1=0$ and $x-y+5=0$ is

Let a circle $C_1 \equiv x^2 + y^2 - 4x + 6y + 1 = 0$ and circle $C_2$ be such that its centre is the image of the centre of $C_1$ about the $x$-axis and the radius of $C_2$ is equal to the radius of $C_1$. Then,the area of $C_1$ which is not common with $C_2$ is:

The circle $x^2 + y^2 + 4x - 4y + 4 = 0$ touches

Suppose that two chords, drawn from the point $(1, 2)$ on the circle $x^2 + y^2 + x - 3y = 0$, are bisected by the $y$-axis. If the other ends of these chords are $R$ and $S$, and the midpoint of the line segment $RS$ is $(\alpha, \beta)$, then $6(\alpha + \beta)$ is equal to: