CUET · MATHS · PYQ PAPER 2023
The area of the region bounded by the parabola \(y^2=4 a x\) and its latus rectum is:
- A \(\frac{4 a^2}{3}\) sq. units
- B \(\frac{8 a^2}{3}\) sq. units
- C \(\frac{2 a^2}{3}\) sq. units
- D \(\frac{9 a^2}{5}\) sq. units
Answer & Solution
Correct Answer
(B) \(\frac{8 a^2}{3}\) sq. units
Step-by-step Solution
Detailed explanation
Area \( = 2 \int_0^a \sqrt{4ax} \, dx \) \( = 2 \int_0^a 2\sqrt{a}x^{1/2} \, dx \) \( = 4\sqrt{a} \left[ \frac{x^{3/2}}{3/2} \right]_0^a \) \( = 4\sqrt{a} \left( \frac{2}{3} a^{3/2} - 0 \right) \) \( = \frac{8}{3} a^{1/2} a^{3/2} \) \( = \frac{8 a^2}{3}\) sq. units
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