If the radical axis of the circles $x^2+y^2+2 \alpha x+2 \beta y+c=0$ and $x^2+y^2+\frac{3}{2} x+4 y+c=0$ touches the circle $x^2+y^2+2 x+2 y+1=0$,then $4 \alpha \beta-8 \alpha-3 \beta+10=$

The distance between the centres of similitude of the circles $x^2+y^2+6x-8y+16=0$ and $x^2+y^2-2x-2y+1=0$ is

If $2 x^{2}+2 y^{2}+4 x+5 y+1=0$ and $3 x^{2}+3 y^{2}+6 x-7 y+3 k=0$ are orthogonal,then the value of $k$ 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

If the angle between the circles $x^2+y^2-2x+2y+1=0$ and $x^2+y^2+2x-2y+k=0$ is $\frac{\pi}{3}$,then

The circle $S=0$ cuts the circle $x^2+y^2-4x+2y-7=0$ orthogonally. If $(2,3)$ is the centre of the circle $S=0$,then its radius is