$A$ line passing through the point $P(3, 11)$ intersects the circle $x^{2} + y^{2} = 9$ at points $A$ and $B$. Then $PA \cdot PB = . . . . .$

Suppose a circle passes through $(2,2)$ and $(9,9)$ and touches the $X$-axis at $P$. If $O$ is the origin,then $OP$ is equal to

The position of the point $(1, 1)$ with respect to the circle $x^2 + y^2 - x + y - 1 = 0$ is:

Let $R$ be the region of the disc $x^2+y^2 \leq 1$ in the first quadrant. Then,the area of the largest possible circle contained in $R$ is

The line $4x - 3y + 2 = 0$ intersects the circle $x^2 + y^2 - 2x + 6y + c = 0$ at two points $A$ and $B$,and the length of the chord $AB = 8$. If $(1, k)$ is a point on the given circle and $k > 0$,then $k =$

$A$ line is drawn through a fixed point $P(\alpha, \beta)$ to cut the circle $x^{2}+y^{2}=r^{2}$ at $A$ and $B$. Then $PA \cdot PB$ is equal to