The line $3x + y - 5 = 0$ touches a circle $S$ at $(1, 2)$. If $(h, k)$ is the centre of the circle $S$ such that $h^2 + hk + k^2 = 37$ and the radius of the circle $S$ is $\sqrt{10}$,then $k =$

$A$ circle with centre $(a, b)$ passes through the origin. The equation of the tangent to the circle at the origin is

When will the line $y = x + c$ intersect the circle $x^2 + y^2 = 1$ at two coincident points?

$A$ 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 normal to the circle $x^2 + y^2 - 2x = 0$ parallel to the line $x + 2y = 3$ is

The angle between the tangents drawn from a point $(4,3)$ to the circle $x^2+y^2-2x-4y=0$ is