The equation of the circle with the origin as the centre passing through the vertices of an equilateral triangle whose median is of length $3a$ is

$ABCD$ is a square with side $16$ units and $A$ is the origin. If the equation of the circle circumscribing the square $ABCD$ is $x^2+y^2=4k(x+y)$,then $k=$

The centre and radius of the circumcircle of the triangle formed by the lines $2x+3y=10$,$y=x$ and the $X$-axis are respectively:

Let the abscissae of the two points $P$ and $Q$ on a circle be the roots of $x^{2}-4x-6=0$ and the ordinates of $P$ and $Q$ be the roots of $y^{2}+2y-7=0$. If $PQ$ is a diameter of the circle $x^{2}+y^{2}+2ax+2by+c=0$,then the value of $(a+b-c)$ is.

What is the length of the diameter of the circle $x^2 + y^2 - 4x - 6y + 4 = 0$?

The equation of the circle passing through $(0,0)$ and which makes intercepts $a$ and $b$ on the coordinate axes is