Q164 / 270 · NDA 2013 (Phase 2) · Mathematics

The length of latus rectum of the ellipse $4 x^2+9 y^2=36$ is

  • A
    $\frac{4}{3}$
  • Correct answer
    B
    $\frac{8}{3}$
  • C
    6
  • D
    12

Solution

Standard equation of ellipse is: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ Length of latus rectum $=\frac{2 b^2}{a}$ Given equation is $4 x^2+9 y^2=36$ or, $\begin{aligned} \frac{x^2}{9}+\frac{y^2}{4} & =1 \\ a^2 & =9, b^2=4 \end{aligned}$ Length of latus rectum $=\frac{2 \times 4}{3}=\frac{8}{3}$

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

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