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The area of the region bounded by the parabola y2=4axy^2 = 4ax and its latus rectum is:

Solution

✅ Correct Option: 2

Latus rectum is the vertical line x=ax = a. Area =2∫0a2ax dx=4a⋅23x3/2∣0a=8a3⋅a3/2=8a23= 2 \int_0^a 2\sqrt{ax}\,dx = 4\sqrt{a} \cdot \frac{2}{3} x^{3/2} \Big|_0^a = \frac{8\sqrt{a}}{3} \cdot a^{3/2} = \frac{8a^2}{3} sq. units.

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