Equation of a sphere is very similar to that of a plane-disc(circular-region).
Consider Origin, O, of the
space to be centre of the sphere of radius r.
Let point P(x,y,z) be a point inside or on the sphere.
Then, you'll have
More generally if C(u,v,w) is the centre
Hence any second degree equation in three variables of sort
represents a sphere of centre C(-u,-v,-w) and radius,