Find the equation of the circle with centre $(-2, 3)$ and radius $4$.

The parametric equations of the circle $2x^2 + 2y^2 = 9$ are

The equation of the circle concentric with the circle $x^2 + y^2 + 8x + 10y - 7 = 0$ and passing through the centre of the circle $x^2 + y^2 - 4x - 6y = 0$ is

Find the equation of the circle which passes through the point $(-2, -7)$ and is concentric with the circle $x^{2} + y^{2} - 8x + 6y - 5 = 0$.

The equation of the circle concentric with the circle $x^2 + y^2 - 6x + 7 = 0$ and which touches the line $x + y + 3 = 0$ is:

Let the equation $x^{2}+y^{2}+px+(1-p)y+5=0$ represent circles of varying radius $r \in (0, 5]$. Then the number of elements in the set $S = \{q : q = p^{2} \text{ and } q \text{ is an integer}\}$ is ..... .