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The hyperbola x²/a² - y²/3 = 1 (eccentricity e) is confocal with the ellipse x²/8 + y²/4 = 1. Let A, B, C, D be the points of intersection of the hyperbola and the ellipse. Which statement is correct?

1. A, B, C, D are concyclic points
2. e = 5/2
3. the number of common tangents is 2
4. e = sqrt(3)

Correct answer: A, B, C, D are concyclic points

Solution

The four intersection points are symmetric about both axes (form a rectangle centred at the origin), so they are concyclic. The eccentricity works out to e = 2, not 5/2 or sqrt(3).

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