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Let LMNP be a non-square rectangle inscribed in an ellipse with the major-axis endpoints A, A', minor-axis endpoints B, B', and the rectangle vertices L, M, N, P. Let lambda be the number of ways of choosing four of the eight points A, A', B, B', L, M, N, P such that the normals to the ellipse at those four chosen points are concurrent. Then lambda is at most:

1. 5
2. 6
3. 7
4. 4

Correct answer: 5

Solution

Sets of four points symmetric about both axes give concurrent normals; counting all such valid quadruples gives 5.

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