If the equation of the circle having the common chord to the circles $x^2+y^2+x-3 y-10=0$ and $x^2+y^2+2 x-y-20=0$ as its diameter is $x^2+y^2+\alpha x+\beta y+\gamma=0$, then $\alpha+2 \beta+\gamma=$

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are $(1,2)$ and $(4,5)$ is

A circle touches both the coordinate axes and the straight line $L \equiv 4 x+3 y-6=0$ in the first quadrant. If this circle lies below the line $L=0$, then the equation of that circle is

If the smallest circle through the points of intersection of $x^2+y^2=a^2$ and $x \cos \alpha+y \sin \alpha=p, 0