If the endpoints of the diameter of a circle are $(4, 3)$ and $(-12, -1)$,then the equation of the circle is . . . . .

If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$,then the equation of the circle is

If three distinct points $A, B, C$ are given in the $2$-dimensional coordinate plane such that the ratio of the distance from $(1, 0)$ to the distance from $(-1, 0)$ is equal to $\frac{1}{2}$,then the circumcentre of the triangle $ABC$ is at the point

The equation of the circle which touches the lines $x = 0$,$y = 0$ and $3x + 4y = 4$ is

The area enclosed by the curve $x = \sqrt{3} \cos \theta, y = \sqrt{3} \sin \theta$ is

The centre of the circle given by the parametric equations $x = -1 + 2\cos \theta$ and $y = 3 + 2\sin \theta$ is: