The points of intersection of two ellipses $x^{2}+2y^{2}-6x-12y+20=0$ and $2x^{2}+y^{2}-10x-6y+15=0$ lie on a circle. The centre of the circle is

If the circle $S \equiv x^2+y^2+2gx+4y+1=0$ bisects the circumference of the circle $x^2+y^2-2x-3=0$,then the radius of circle $S=0$ is

If $T_1 T_1^{\prime}$ and $T_2 T_2^{\prime}$ are the common tangents of the circles $S = x^2 + y^2 - 2x - 4y - 4 = 0$ and $S^{\prime} = x^2 + y^2 + 4x + 4y + 4 = 0$, where $T_1, T_1^{\prime}, T_2, T_2^{\prime}$ are the points of contact, then the distance between $T_1$ and $T_1^{\prime}$ is (in $\sqrt{6}$)

The equation of the circle which passes through the point of intersection of circles $x^2 + y^2 - 8x - 2y + 7 = 0$ and $x^2 + y^2 - 4x + 10y + 8 = 0$ and has its centre on the $y$-axis is:

Find the equation of the circle passing through the intersection of the circles $x^{2} + y^{2} - 8x - 2y + 7 = 0$ and $x^{2} + y^{2} - 4x + 10y + 8 = 0$,and having its center on the $y-$axis.

If one of the diameters of the circle $x^2+y^2-10x+4y+13=0$ is a chord of another circle $C$,whose center is the point of intersection of the lines $2x+3y=12$ and $3x-2y=5$,then the radius of the circle $C$ is