When does the equation $x^2 + y^2 + 2gx + 2fy + c = 0$ represent a point circle?

The radius of the larger circle lying in the first quadrant and touching the line $4x + 3y - 12 = 0$ and the coordinate axes is:

The equation of the circumcircle of the quadrilateral formed by the lines $x = a, x = 2a, y = -a, y = a$ is:

The four distinct points $(0, 0), (2, 0), (0, -2)$ and $(k, -2)$ are concyclic,if $k =$

If the parametric equations of the circle passing through the points $(3,4)$,$(3,2)$,and $(1,4)$ are $x=a+r \cos \theta$ and $y=b+r \sin \theta$,then find the value of $b^{a} r^{a}$.

If the vertices of a triangle are $(2, -2)$,$(-1, -1)$,and $(5, 2)$,then the equation of its circumcircle is