Find the centre and radius of the circle $(x+5)^{2}+(y-3)^{2}=36$.

The equation of the circle which touches both the axes and whose radius is $a$ is

The diameters of a circle are along $2x + y - 7 = 0$ and $x + 3y - 11 = 0$. Then,the equation of this circle,which also passes through $(5, 7)$,is

The equation of the circle which passes through the points $(2, 3)$ and $(4, 5)$ and whose centre lies on the straight line $4x - y - 3 = 0$ is:

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:

The equation of the circle passing through the point $(2, 1)$ and touching the $y$-axis at the origin is: