If the angle between the circles $x^2+y^2-4x-6y+k=0$ and $x^2+y^2+8x-4y+11=0$ is $\frac{\pi}{2}$,then the value of $k$ is

Find the equation of the circle whose diameter is the common chord of the circles $x^2 + y^2 - 8x + y - 15 = 0$ and $x^2 + y^2 - 4x + 4y - 42 = 0$.

If the circles $x^2 + y^2 + 2ax + c = 0$ and $x^2 + y^2 + 2by + c = 0$ touch each other,then:

If one of the diameters of the curve $x^{2}+y^{2}-4x-6y+9=0$ is a chord of a circle with centre $(1,1)$, the radius of this circle is

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

The centre of the circle touching the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$ at their point of contact and passing through the point $(1, -1)$ is