Q168 / 270 · NDA 2014 (Phase 2) · Mathematics

What is the length of the latus rectum of the ellipse $25 x^2+16 y^2=400$ ?

  • A
    $\frac{25}{2}$
  • B
    $\frac{25}{4}$
  • C
    $\frac{16}{5}$
  • Correct answer
    D
    $\frac{32}{5}$

Solution

$\frac{25 x^2}{400}=\frac{16 y^2}{400}=\frac{400}{400} \Rightarrow \frac{x^2}{16}+\frac{y^2}{25} \quad=1$ Length of latus rectum of ellipse $=\frac{2 a^2}{b}=\frac{2 \times 16}{5}=\frac{32}{5}$.

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

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