Tangents to a circle at points $P$ and $Q$ on the circle intersect at a point $R$. If $PQ=6$ and $PR=5$,then the radius of the circle is

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 $k =$

The equation of the circle which touches the circle ${x^2 + y^2 - 6x + 6y + 17 = 0}$ externally and to which the lines ${x^2 - 3xy - 3x + 9y = 0}$ are normals,is

If $\theta$ is the angle between the tangents drawn from the point $(2,3)$ to the circle $x^2+y^2-6x+4y+12=0$,then $\theta=$

The line $x + y = 2$ is tangent to the curve $x^2 = 3 - 2y$ at its point

Match the points on the curve $2y^2 = x + 1$ with the slopes of the normals at those points and choose the correct answer.

$A. (7, 2)$	$1. -4\sqrt{2}$
$B. (0, 1/\sqrt{2})$	$2. -8$
$C. (1, -1)$	$3. 4$
$D. (3, \sqrt{2})$	$4. 0$
	$5. -2\sqrt{2}$