If the area of the circum-circle of triangle formed by the line $2 x+5 y+\alpha=0$ and the positive coordinate axes is $\frac{29 \pi}{4} S q$, units, then $|\alpha|=$

The circle $S \equiv x^2+y^2-2 x-4 y+1=0$ cuts the $Y$-axis at $A, B(O A>O B)$. If the radical axis of $S \equiv 0$ and $S' \equiv x^2+y^2-4 x-2 y+4=0$ cuts the $Y$-axis at $C$, then the ratio in which $C$ divides $A B$ is

If the circle $S=0$ cuts the circles $x^2+y^2-2 x+6 y=0$, $x^2+y^2-4 x-2 y+6=0$ and $x^2+y^2-12 x+2 y+3=0$ orthogonally, then equation of the tangent at $(0,3)$ on $S=0$ is

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