Tangent Planes to an ellipsoid

Calculus Level 5

An ellipsoid is given by

\[ \dfrac{x^2}{100} + \dfrac{y^2}{225} + \dfrac{z^2}{625} = 1 \]

Consider the tangent planes to this ellipsoid that pass through the points \( (10, 15, 20) \) and \( (-5, -10, 40) \). There are only two such planes. Find the angle between them in degrees rounded to the nearest tenth of a degree.

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