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\section*{Equations}  The equation for a ellipsoid with axises $e_1, e_2$ and $e_3$:  $$E(x) := \frac{x_1^2}{e_1^2} + \frac{x_2^2}{e_2^2} + \frac{x_3^2}{e_3^2} - 1 = 0$$  Let $y = \begin{bmatrix} y_1 & y_2 & y_3 \end{bmatrix}^T$ be a point outside the ellipsoid.  For any point $x = \begin{bmatrix} x_1 & x_2 & x_3 \end{bmatrix}^{T}$ on the ellipsoid we have\footnote{http://www.geometrictools.com/Documentation/DistancePointEllipseEllipsoid.pdf}: 
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