The value of $\lambda$,for which the circle $x^2 + y^2 + 2\lambda x + 6y + 1 = 0$ intersects the circle $x^2 + y^2 + 4x + 2y = 0$ orthogonally is

If one of the diameters of the circle $x^2+y^2-10x+4y+13=0$ is a chord of another circle $C$,whose center is the point of intersection of the lines $2x+3y=12$ and $3x-2y=5$,then the radius of the circle $C$ is

$P$ is a point of intersection of the circles $S \equiv x^2+y^2-6x+2ky+1=0$ and $S' \equiv x^2+y^2+2kx-6y-7=0$. If the tangent at $P$ to $S=0$ passes through the centre of $S'=0$ and the tangent at $P$ to $S'=0$ passes through the centre of $S=0$,then the radius of $S'=0$ is

The number of common tangents to the circles $x^2 + y^2 - 8x - 2y + 1 = 0$ and $x^2 + y^2 + 6x + y = 0$ is:

$C_1$ and $C_2$ are the external and internal centres of similitude of the circles $x^2+y^2-2x+4y+1=0$ and $x^2+y^2+4x-6y+12=0$. If the radius of the circle having $C_1C_2$ as its diameter is $r$,then $\frac{9}{2}r=$

The gradient of the radical axis of the circles ${x^2} + {y^2} - 3x - 4y + 5 = 0$ and $3{x^2} + 3{y^2} - 7x + 8y + 11 = 0$ is