The radius of a circle with center $(a, b)$ and passing through the center of the circle $x^2 + y^2 - 2gx + f^2 = 0$ is:

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

The lines $2x - 3y = 5$ and $3x - 4y = 7$ are the diameters of a circle of area $154$ square units. The equation of the circle is

Let the abscissae of the two points $P$ and $Q$ be the roots of $2x^{2}-rx+p=0$ and the ordinates of $P$ and $Q$ be the roots of $y^{2}-sy-q=0$. If the equation of the circle described on $PQ$ as diameter is $2(x^{2}+y^{2})-11x-14y-22=0$,then $2r+s-2q+p$ is equal to

The equation of the circle which passes through the points $(2, 3)$ and $(4, 5)$ and whose centre lies on the straight line $y - 4x + 3 = 0$ is:

Find the equation of the circle which passes through the point $(-2, -7)$ and is concentric with the circle $x^{2} + y^{2} - 8x + 6y - 5 = 0$.