If $P(\frac{\pi}{3})$ and $Q(\frac{2\pi}{3})$ represent two points on the circle $x^2+y^2-4x+6y-12=0$ in parametric form,then the length of the chord $PQ$ is

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:

$A$ square is inscribed in the circle $x^2+y^2-2x+4y-93=0$ with its sides parallel to the coordinate axes. Which of the following can be one of the vertices of the square?

The two circles $x^2 + y^2 - 4y = 0$ and $x^2 + y^2 - 8y = 0$:

If the power of the point $(1, 6)$ with respect to the circle $x^2 + y^2 + 4x - 6y - a = 0$ is $-16$,then $a$ equals:

The number of circles having radius $5$ and passing through the points $(-2, 0)$ and $(4, 0)$ is