The equation obtained by transforming $x^2+y^2-6x+10y-2=0$ to the parallel axes through $(3,-5)$ is

The equation of a circle which touches the $x$-axis and whose centre is $(1, 2)$ is

$A$ 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?

Find the equation of the circle passing through the points $(2, 3)$ and $(-1, 1)$ and whose centre is on the line $x - 3y - 11 = 0$.

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

If the lines $2x + 3y + 1 = 0$ and $3x - y - 4 = 0$ are diameters of a circle with circumference $10\pi$,find the equation of the circle.