A sphere from its equation

You will write three functions about spheres. The checker uses the sphere of the lesson and some points.

The idea. In $x^2 + y^2 + z^2 + 2ux + 2vy + 2wz + d = 0$ the centre is $(-u, -v, -w)$ and $r^2 = u^2 + v^2 + w^2 - d$. A point is on the sphere if its distance from the centre equals $r$.

Your tasks.

1. Finish centre_and_radius(u, v, w, d). Return a tuple (centre, radius). If $r^2 \le 0$ return (centre, None).
2. Finish position(p, centre, r). Return "inside", "on" or "outside". Compare squared distances, and treat differences smaller than 1e-9 as equal.
3. Finish integer_points(r_squared). Count the points with whole-number coordinates that satisfy $x^2 + y^2 + z^2 = r^2$. Search with each coordinate from -10 to 10.