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The normal at a variable point P on the ellipse x²/a² + y²/b² = 1 (eccentricity e) meets the two axes of the ellipse at Q and R. The locus of the midpoint of QR is a conic whose eccentricity e' satisfies which of the following?

1. e' is independent of e
2. e' = 1
3. e' = e
4. e' = 1/e

Correct answer: e' = e

Solution

Eliminating the parameter from the midpoint coordinates yields an ellipse similar to the original, so its eccentricity equals e.

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