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Equation of a sphere is very similar to that of a plane-disc(circular-region).
Consider Origin, O, of the \text{R^{3}} 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
OP \leq r
 \sqrt{x^{2}+y^{2}+z^{2}} \leq r \\
\Rightarrow x^{2}+y^{2}+z^{2} \leq r^{2}.
More generally if C(u,v,w) is the centre (x-u)^{2}+(y-v)^{2}+(z-w)^{2} \leq r^{2}
Hence any second degree equation in three variables of sort 
x^{2}+y^{2}+z^{2}+2ux+2vy+2wz+c \leq 0 represents a sphere of centre C(-u,-v,-w) and radius, r=\sqrt{u^{2}+v^{2}+z^{2}-c}.
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