The common chord of the circles $x^2 + y^2 + 4x + 1 = 0$ and $x^2 + y^2 + 6x + 2y + 3 = 0$ is

If the circles $x^2 + y^2 + 2ax + cy + a = 0$ and $x^2 + y^2 - 3ax + dy - 1 = 0$ intersect in two distinct points $P$ and $Q$,then the line $5x + by - a = 0$ passes through $P$ and $Q$ for

The equation of the common chord of the circles $x^2+y^2+2x+3y+1=0$ and $x^2+y^2-5x-6y+4=0$ is

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

The radius of the circle whose diameter is the common chord of the circles $x^2+y^2+2x+2y+1=0$ and $x^2+y^2+4x+3y+2=0$ is

If the common chord of the circles $x^2+y^2-2x+2y+1=0$ and $x^2+y^2-2x-2y-2=0$ is the diameter of a circle $S$,then the centre of the circle $S$ is