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If the curves x²/a + y²/4 = 1 and y³ = 16x intersect at right angles, then a possible value of a is

1. 4/3
2. 3/4
3. 1/2
4. 2

Correct answer: 4/3

Solution

Differentiating the ellipse gives slope -4x/(a y); differentiating y³ = 16x gives slope 16/(3y²). Orthogonality and the curve equations lead to a = 4/3.

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