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Let F1(x1, 0) with x1 < 0 and F2(x2, 0) with x2 > 0 be the foci of the ellipse x²/9 + y²/8 = 1. A parabola with vertex at the origin and focus at F2 meets the ellipse at M (first quadrant) and N (fourth quadrant). Find the orthocentre of triangle F1MN.

1. (-9/10, 0)
2. (2/3, 0)
3. (9/10, 0)
4. (2/3, sqrt(6))

Correct answer: (9/10, 0)

Solution

Solving the ellipse and parabola y² = 4x gives M = (3/2, sqrt6) and N = (3/2, -sqrt6); the orthocentre of triangle F1MN works out to (9/10, 0).

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