Q57 / 120 · NDA 2024 (Phase 2) · Mathematics

The foci of the ellipse $4 x^2+9 y^2=1$ are at Q and R . If $\mathrm{P}(x, y)$ is any point on the ellipse, then what is $\mathrm{PQ}+\mathrm{PR}$ equal to?

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

Solution

Given equation of ellipse, $4 x^2+9 y^2=1$ Here, $\mathrm{a}=\frac{1}{2}$ and $\mathrm{b}=\frac{1}{3}$ Since, $\mathrm{P}(\mathrm{x}, \mathrm{y})$ is any point on the ellipse. So, $\mathrm{PQ}+\mathrm{PR}=2 \mathrm{a}=2 \times \frac{1}{2}=1$.

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

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