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NDA 2018 Maths · Mathematics · Straight Lines · medium

The latus rectum of an ellipse is half of its minor axis. The eccentricity of the ellipse is

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The latus rectum of an ellipse is half of its minor axis. The eccentricity of the ellipse is
  1. A. 32\frac{\sqrt3}{2}
  2. B. 12\frac12
  3. C. 12\frac{1}{\sqrt2}
  4. D. 34\frac{\sqrt3}{4}
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Answer: (A) 32\frac{\sqrt3}{2}

The latus rectum is 2b2a\frac{2b^2}{a} and the minor axis is 2b2b, so 2b2a=b\frac{2b^2}{a}=b, giving b=a2b=\frac a2. Then e=1−b2a2=1−14=32e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac14}=\frac{\sqrt3}2. The value 12\frac12 is ba\frac ba, not the eccentricity.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake