The points of intersection of the line $4x - 3y - 10 = 0$ and the circle $x^2 + y^2 - 2x + 4y - 20 = 0$ are

Lines are drawn from a point $P(-1, 3)$ to a circle $x^2 + y^2 - 2x + 4y - 8 = 0$. If the line meets the circle at two points $A$ and $B$,then the minimum value of $PA + PB$ is:

$A$ cow is tied to a post by a rope. The cow moves along a circular path,always keeping the rope tight. If it describes an arc of $44 \ m$ when it has traced out $72^{\circ}$ at the centre,the length of the rope is: (in $m$)

Let $\theta$ be the angle between the circles $S \equiv x^2+y^2+2x-2y+c=0$ and $S' \equiv x^2+y^2-6x-8y+9=0$. If $c$ is an integer and $\cos \theta = \frac{5}{16}$,then the radius of the circle $S=0$ is

If the angle between the tangents drawn to the circle $x^2+y^2-12x-16y=0$ at the points where the line $5y=5x+k$ cuts the circle is $60^{\circ}$,then the value of $k$ is

Suppose a circle passes through $(0, a)$ and $(b, h)$ having its centre at $(c, 0)$. Then the value of $c$ is