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

If the radical centre of the three circles $x^2+y^2=1$,$x^2+y^2-2x-3=0$,and $x^2+y^2-2y-3=0$ is $C(\alpha, \beta)$ and $r$ is the sum of the radii of the given circles,then the equation of the circle with $C(\alpha, \beta)$ as centre and $r$ as radius is:

Find the equation of the radical axis of the two circles $x^2 + y^2 - x + 1 = 0$ and $3(x^2 + y^2) + y - 1 = 0$.

The co-axial system of circles given by ${x^2} + {y^2} + 2gx + c = 0$ for $c < 0$ represents

If the circles $x^2+y^2-4x+2fy+1=0$ and $x^2+y^2+2gx-4y-1=0$ cut orthogonally,then $r_1^2+r_2^2-8=$

If the circle $S=0$ intersects the three circles $S_1 \equiv x^2+y^2+4x-7=0$,$S_2 \equiv x^2+y^2+y=0$ and $S_3 \equiv x^2+y^2+\frac{3}{2}x+\frac{5}{2}y-\frac{9}{2}=0$ orthogonally,then the radical axis of $S=0$ and $S_1=0$ is