The radius of the circle with the polar equation $r^2-8r(\sqrt{3} \cos \theta + \sin \theta) + 15 = 0$ is

$A$ circle has its equation in the form $x^2 + y^2 + 2x + 4y + 1 = 0$. Choose the correct coordinates of its centre and the right value of its radius from the following:

Let the circle $S$ which is concentric with the circle $x^2+y^2-2x+ky+4=0$ pass through the point $(3,-2)$. If one of the diameters of $S$ lies along the line $3x-2y+4=0$,then the radius of the circle $S$ is

Find the equation of the circle with centre $\left(\frac{1}{2}, \frac{1}{4}\right)$ and radius $\frac{1}{12}$.

If the parametric equations of the circle passing through the points $(3,4)$,$(3,2)$,and $(1,4)$ are $x=a+r \cos \theta$ and $y=b+r \sin \theta$,then find the value of $b^{a} r^{a}$.

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