Q207 / 270 · NDA 2023 (Phase 1) · Mathematics

Paragraph: Consider the following for the next two (02) items that follow: $\mathrm{P}(x, y)$ is any point on the ellipse $x^2+4 y^2=1$. Let $E, F$ be the foci of the ellipse.
Question: What is $P E+P F$ equal to?

  • A
    $1$
  • Correct answer
    B
    $2$
  • C
    $3$
  • D
    $4$

Solution

$x^2+4 y^2=1$ $\frac{x^2}{1}+\frac{y^2}{\left(\frac{1}{4}\right)}=1$ $a^2=1, b^2=\frac{1}{4}$ $\Rightarrow a=1, b=\frac{1}{2}$ $\because \quad E$ and $F$ are foci $\therefore \quad P E+P F=2 a=$ major axis $=2(1)=2$.

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

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