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

If the radius of a circle $x^{2}+y^{2}-4x+6y-k=0$ is $5$,then $k=$

If the equation $ax^2 + by^2 + 2hxy + 2gx + 2fy + c = 0$ represents a circle passing through the origin,then

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

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

If the radius of a circle is $a$ and it touches the $X$-axis at the origin,then its equation is....