[b]Derivation of the standard form of the equation of a sphere in 3-space: [/b][br][br]A sphere with center ([i]a[/i], [i]b[/i], [i]c[/i]) with radius [i]r [/i]that passes through point ([i]x[/i], [i]y[/i], [i]z[/i]) has equation[br][math]\left(x-a\right)^2+\left(y-b\right)^2+\left(z-c\right)^2=r^2[/math]. [br]