The normal to an ellipse at a point P intersects the ellipse at another point Q. The angle corresponding to Q can be found by solving the equation (P - Q)·(d P)/(d t) = 0 for t', where P(t) = (a cos t, b sin t) and Q(t) = (a cos t', b sin t'). This gives solutions t' = ± cos^(-1)[ ± (N(t))/(a^4 sin^2 t + b^4 cos^2 t)], where N(t) congruent 1/2 b^2 cos t[a^2 + b^2 + (b^2 - a)^2 cos(2t)] + a^2(a - b)(a + b) cos t sin^2 t, of which (+, - ) gives the valid solution.
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