Which of the following lines is a tangent to the circle $x^2 + y^2 = 25$ for all values of $m$?

If the length of the tangent drawn from the point $(5, 3)$ to the circle $x^2 + y^2 + ky + 17 = 0$ is $7$,then $k = \dots$

Let the tangents at the points $A (4, -11)$ and $B (8, -5)$ on the circle $x^2 + y^2 - 3x + 10y - 15 = 0$ intersect at the point $C$. Then the radius of the circle,whose center is $C$ and the line joining $A$ and $B$ is its tangent,is equal to

$A$ circle is such that $(x-2) \cos \theta + (y-2) \sin \theta = 1$ touches it for all values of $\theta$. Then,the circle is

If the tangent drawn at the point $P$ on the circle $x^2+y^2+6x+6y=2$ meets the straight line $5x-2y+6=0$ at a point $Q$ on the $Y$-axis,then the length of $PQ$ is

If the straight line $y = mx + c$ touches the circle $x^2 + y^2 - 2x - 4y + 3 = 0$ at the point $(2, 3)$,then $c =$