The point of intersection of the common tangents drawn to the circles $x^2+y^2-4x-2y+1=0$ and $x^2+y^2-6x-4y+4=0$ is:

Suppose $A(2,3)$ and $B$ are the points of intersection of two circles. The points $P$ lying on one circle and $Q$ lying on the other circle are such that $BP$ and $BQ$ constitute the diameters of the circles. If the slopes of the radical axis and $PQ$ are $3/4$ and $a/b$ respectively,then the value of $3a+4b$ is

The straight line $x \cos \alpha + y \sin \alpha = p$ cuts the circle $x^2 + y^2 - a^2 = 0$ at $A$ and $B$. Then the equation of the circle having $AB$ as diameter is

If one of the diameters of the circle $x^{2}+y^{2}-2x-6y+6=0$ is a chord of another circle $'C'$,whose center is at $(2,1)$,then its radius is..........

If the circles $C_1: x^2+y^2+2x+4y-20=0$ and $C_2: x^2+y^2+6x-8y+9=0$ have $n$ common tangents and the length of the tangent drawn from the centre of similitude to the circle $C_2$ is $l$,then $\frac{l}{n^2} =$

The ratio of the areas of the greatest and the smallest circles touching $(x \pm 1)^2 + (y \pm 1)^2 = 1$ is