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On the ellipse 4x² + 9y² = 36, find a point at which the normal is parallel to the line 4x - 2y - 5 = 0.

1. (9/5, -8/5)
2. (-9/5, 8/5)
3. (8/5, 9/5)
4. (9/5, 8/5)

Correct answer: (9/5, 8/5)

Solution

Setting the normal slope (9y0)/(4x0) = 2 with the point on the ellipse gives y = 8x/9; solving yields (9/5, 8/5) (and its diametric opposite), so (9/5, 8/5) is the listed point.

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