deletions | additions       diff --git a/The_equation_for_the_ellipsoid__.tex b/The_equation_for_the_ellipsoid__.tex  index 9ae9dad..21b9448 100644  --- a/The_equation_for_the_ellipsoid__.tex  +++ b/The_equation_for_the_ellipsoid__.tex 
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$$E(x) := \frac{x_1^2}{e_1^2} + \frac{x_2^2}{e_2^2} + \frac{x_3^2}{e_3^2} - 1 = 0$$  Let $y$ be a point outside the ellipsoid:  $$y = \begin{bmatrix} y_1 \\ y_2 \\ y_3 \end{bmatrix}$$  For any point $x$ $x = \begin{bmatrix} x_1 & x_2 & x_3 \end{bmatrix}^{T}$  on the ellipsoid we have: $$y - x = \frac{1}{2} t \nabla E(x)   = t \begin{bmatrix}   \frac{1}{e_1^2} && \\  
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