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

The Cartesian equation of the curve $x=3+5 \cos \theta, y=2+5 \sin \theta$ is $(0 \leq \theta \leq 2 \pi)$.

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:

Let $S$ be a circle concentric with the circle $3x^2+3y^2+x+y-1=0$. If the length of the tangent drawn from a point $(2,-2)$ to the given circle is the radius of the circle $S$,then the power of the point $(2,1)$ with respect to the circle $S$ is

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

Find the equation of the circle with centre $(-3, 2)$ and radius $4$.