If the circles $x^2+y^2-6x-8y-12=0$ and $x^2+y^2-4x+6y+k=0$ are orthogonal to each other,then the value of $k$ is:

Consider the system of circles $x^2+y^2+2fy+\lambda(x^2+y^2+2gx+k)=0$,where $g \neq 0, f \neq 0$ and $\lambda$ is a parameter. If $A$ and $B$ are the point circles of this system such that $\angle AOB = \frac{\pi}{2}$,then $g^2$ is equal to

If the line $y = x + 3$ intersects the circle $x^2 + y^2 = a^2$ at two points $A$ and $B$,then the equation of the circle having $AB$ as its diameter is . . . . . .

The internal centre of similitude of the two circles $x^2+y^2-4x-6y+12=0$ and $x^2+y^2+4x-2y-4=0$ is

The straight line $x+y-1=0$ meets the circle $x^2+y^2-6x-8y=0$ at $A$ and $B$. Then the equation of the circle of which $AB$ is a diameter is

The equation of the circle which passes through the point $(1, 1)$ and intersects the given circles $x^2 + y^2 + 2x + 4y + 6 = 0$ and $x^2 + y^2 + 4x + 6y + 2 = 0$ orthogonally is: