The radius of the circle $x^2 + y^2 + 4x + 6y + 13 = 0$ is

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

The polar equation of the circle with centre $\left(2, \frac{\pi}{2}\right)$ and radius $3$ units is :

The equation of the circle,concentric with the circle $2x^2+2y^2-6x+8y+1=0$ and having double its area,is

$A$ circle of radius $5$ units touches the axes in the first quadrant. If the circle rolls along the $x-$axis in the positive $x-$direction for one complete revolution,find its equation in the new position.

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