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View submission: Ask Anything Wednesday - Engineering, Mathematics, Computer Science
To elaborate slightly on the matrix transformation aspect: the thought there is to take the problem from a point on an arbitrarily oriented ellipse (which, as you've noted, is rather difficult) to a point on a much easier to work with ellipse (that is, one aligned with your coordinate axes). This is done by noting that it's a simple frame rotation to go from one ellipse to the other, so you can solve the easier problem and then apply the same rotation to translate the solution to the harder problem.
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