Q235 / 270 · NDA 2022 (Phase 1) · Mathematics

What is the distance between the foci of the ellipse $x^2+2 y^2=1$ ?

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

Solution

Given equation of ellipse $\begin{aligned} & x^2+2 y^2=1 \Rightarrow \frac{x^2}{1}+\frac{y^2}{\frac{1}{2}}=1 \\ & \Rightarrow a^2=1 \text { and } b^2=\frac{1}{2}\end{aligned}$ $\begin{aligned} & \because \mathrm{b}^2=\mathrm{a}^2-\mathrm{c}^2 \\ & \mathrm{c}^2=\mathrm{a}^2-\mathrm{b}^2=1-\frac{1}{2}=\frac{1}{2} \\ & \mathrm{c}=\frac{1}{\sqrt{2}}\end{aligned}$ The distance between foci of ellipse $=2 \mathrm{C}=\frac{2}{\sqrt{2}}=\sqrt{2}$

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

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