If $A, B$ are the points of contact of the tangents drawn from the point $P(-2,-3)$ to the circle $x^2+y^2-8 x-10 y+5=0$ and the chord $A B$ subtends an angle $\theta$ at $P$, then $\tan \theta=$

The equation of the transverse common tangent of the circles $x^2+y^2-6 x-8 y+9=0$ and $x^2+y^2+2 x-2 y+1=0$

If $\theta$ is the angle between the circles

$x^2+y^2-2 x-4 y-4=0$ and $x^2+y^2-8 x-12 y+43=0$, then $|7 \sec \theta-18 \cos \theta|=$

If $\left(0, \frac{3}{4}\right)$ is the radical centre of the circles $S \equiv x^2+y^2+\alpha x+6 y=0, S \equiv x^2+y^2+2 \alpha x+\alpha y+6=0$ and $S^{\prime \prime} \equiv x^2+y^2+6 \alpha x-\alpha y+3=0$, then the distance between the radical centre and the centre of the circle $S^{\prime}=0$ is