Q88 / 120 · NDA 2024 (Phase 2) · Mathematics

Paragraph: The area bounded by the parabola $y^2=k x$ and the line $x=k$, where $k>0$, is $\frac{4}{3}$ square units.
Question: What is the area of the parabola bounded by the latus rectum?

  • Correct answer
    A
    $\frac{1}{6}$ square unit
  • B
    $\frac{2}{3}$ square unit
  • C
    1 square unit
  • D
    $\frac{4}{3}$ square unit

Solution

So equation of parabola is $\mathrm{y}^2=\mathrm{x}(\mathrm{k}=1)$ $4 a=1, a=\frac{1}{4}$ Area of parabola $\mathrm{y}^2=\mathrm{x}$ and latus rectum at $\mathrm{x}=\frac{1}{4}$ is $=2 \int_0^{\frac{1}{4}} \sqrt{\mathrm{x}} \mathrm{dx}=2 \times \frac{2}{3}\left(\frac{1}{4}\right)^{\frac{3}{2}}=\frac{4}{3} \times \frac{1}{8}=\frac{1}{6}$ sq. units

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

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