The radical axis of the circles $x^2+y^2+5x+4y-5=0$ and $x^2+y^2-3x+5y-6=0$ is:

If $P$ and $Q$ are the points of intersection of the circles $x^2 + y^2 + 3x + 7y + 2p - 5 = 0$ and $x^2 + y^2 + 2x + 2y - p^2 = 0$,then for what value of $p$ does a circle pass through $P, Q$ and $(1, 1)$?

If the circle $x^2 + y^2 = 4$ bisects the circumference of the circle $x^2 + y^2 - 2x + 6y + a = 0$,then $a$ equals

The equation of the circle which passes through the intersection of ${x^2} + {y^2} + 13x - 3y = 0$ and $2{x^2} + 2{y^2} + 4x - 7y - 25 = 0$ and whose centre lies on $13x + 30y = 0$ is

The limiting points of the co-axial system containing the two circles $x^2+y^2+2x-2y+2=0$ and $25(x^2+y^2)-10x-80y+65=0$ are

$A$ circle $C$ passing through the point $(1, 1)$ bisects the circumference of the circle $x^2+y^2-2x=0$. If $C$ is orthogonal to the circle $x^2+y^2+2y-3=0$,then the centre of the circle $C$ is