Find the centre and radius of the circle $x^{2}+y^{2}-4x-8y-45=0$.

$A$ circle has a radius of $3$ units and its centre lies on the line $y = x - 1$. If the circle passes through the point $(7, 3)$,what is its equation?

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

If $(1, 1), (-2, 2), (2, -2)$ are $3$ points on a circle $S$,then the perpendicular distance from the centre of the circle $S$ to the line $3x - 4y + 1 = 0$ is

If the segments of the straight lines $x+y=6$ and $x+2y=4$ are two diameters of a circle passing through $(6,2)$,then the equation of that circle is

The circle possessing $y$-axis as its tangent at $(0,2)$ and passing through $(-1,0)$,also passes through