If $(\alpha, \beta)$ is the external centre of similitude of the circles $x^2+y^2=3$ and $x^2+y^2-2x+4y+4=0$,then $\frac{\beta}{\alpha}=$

If the lengths of tangents drawn from a point $P$ to the circles $x^2+y^2-8x+40=0$,$5x^2+5y^2-25x+80=0$,and $x^2+y^2-8x+16y+160=0$ are equal,then the point $P$ is:

The equation of the circle passing through the points of intersection of the circles $x^2 + y^2 - 6x + 8 = 0$ and $x^2 + y^2 - 6 = 0$ and the point $(1, 1)$ is:

If one of the diameters of the circle $x^{2}+y^{2}-2x-6y+6=0$ is a chord of another circle $'C'$,whose center is at $(2,1)$,then its radius is..........

If one of the diameters of the circle,given by the equation $x^2+y^2-4x+6y-12=0$,is a chord of a circle,$S$,whose centre is at $(-3,2)$,then the length of the radius of $S$ is . . . . . . units.

The length of the tangent drawn from any point on the circle $x^2+y^2+2gx+2fy+c_1=0$ to the circle $x^2+y^2+2gx+2fy+c_2=0$ is