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Let e1 and e2 be the eccentricities of the ellipse x²/18 + y²/4 = 1 and the hyperbola x²/9 - y²/4 = 1 respectively. If the point (e1, e2) lies on the curve 15x² + 3y² = k, find k.

1. 16
2. 15
3. 14
4. 17

Correct answer: 16

Solution

e1² = 1 - 4/18 = 7/9 and e2² = 1 + 4/9 = 13/9; then k = 15*(7/9) + 3*(13/9) = 16.

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