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Let A(alpha) and B(beta) be endpoints of a chord of an ellipse (eccentric angles alpha, beta). If the slope of chord AB equals the slope of the tangent at the point C(theta) on the ellipse, find theta.

1. (alpha + beta)/2
2. (alpha - beta)/2
3. (alpha + beta)/2 + pi
4. (alpha - beta)/2 - pi

Correct answer: (alpha + beta)/2

Solution

Equating chord slope -(b/a)cot((alpha+beta)/2) with tangent slope -(b/a)cot(theta) gives theta = (alpha+beta)/2.

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