The circle represented by the equation $x^2 + y^2 + 2gx + 2fy + c = 0$ will be a point circle,if

Find the equation of the circle with radius $5$ whose centre lies on the $x-$axis and passes through the point $(2, 3)$.

The equation of the circle with centre at $(1, -2)$ and passing through the centre of the given circle $x^2 + y^2 + 2y - 3 = 0$ is

For what value of $t$ do the four distinct points $(2, 3), (0, 2), (4, 5),$ and $(0, t)$ lie on a circle?

The abscissae of two points $A$ and $B$ are the roots of the equation $x^2+2ax-b^2=0$ and their ordinates are roots of the equation $y^2+2py-q^2=0$. Then the equation of the circle with $AB$ as diameter is given by

The radius of the circle $x^2 + y^2 + 4x + 6y + 13 = 0$ is