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For the ellipse x²/16 + y²/25 = 1, the perpendicular distance from the origin (centre) to any normal of the ellipse is l. Which of the following is a value that l CANNOT take?

1. 4
2. 5/2
3. 1/2
4. 2/3

Correct answer: 4

Solution

The distance from the centre to a normal of the ellipse cannot exceed |larger semi-axis - smaller semi-axis| = 5 - 4 = 1, so l = 4 is impossible (and even 5/2 exceeds 1; among the options 4 is the clearly impossible value).

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