If the line $lx + my + n = 0$ is a tangent to the circle $(x - h)^2 + (y - k)^2 = a^2$,then

If $3x + y + k = 0$ is a tangent to the circle $x^2 + y^2 = 10$,then $k = . . . . . . $.

The two circles which pass through $(0, a)$ and $(0, -a)$ and touch the line $y = mx + c$ will intersect each other at a right angle,if

If the tangent to the conic $y - 6 = x^2$ at $(2, 10)$ touches the circle $x^2 + y^2 + 8x - 2y = k$ (for some fixed $k$) at a point $(\alpha, \beta)$,then $(\alpha, \beta)$ is

$A$ circle $C_{1}$ passes through the origin $O$ and has a diameter of $4$ on the positive $x$-axis. The line $y = 2x$ intersects the circle $C_{1}$ at $O$ and $A$. Let $C_{2}$ be the circle with $OA$ as a diameter. If the tangent to $C_{2}$ at the point $A$ meets the $x$-axis at $P$ and the $y$-axis at $Q$,then the ratio $QA : AP$ is equal to:

The equation of the tangent to the circle $x^2 + y^2 = 25$ which is inclined at an angle of $60^{\circ}$ with the $x$-axis is: