Q178 / 270 · NDA 2012 (Phase 1) · Mathematics

If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity?

  • A
    $2 / \sqrt{3}$
  • B
    $1 / \sqrt{3}$
  • Correct answer
    C
    $\sqrt{3} / 2$
  • D
    $1 / \sqrt{2}$

Solution

$\begin{aligned} \frac{2 b^2}{a} & =b \\ 2 b & =a \\ b^2 & =a^2\left(1-e^2\right) \\ b^2 & =4 b^2\left(1-e^2\right) \\ \frac{1}{4} & =1-e^2 \\ e^2 & =1-\frac{1}{4}=\frac{3}{4} \\ e & =\frac{\sqrt{3}}{2} .\end{aligned}$

Hence, the correct answer is option: 'C'.

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