Area bounded by the parabola y2 = 4ax and its latus-rectum is:

Question

Area bounded by the parabola $y^{2} = 4 a x$ and its latus-rectum is:

Smart Achievers · Accepted Answer

(3)

Ans. $\frac{8}{3} a^{2}$ sq. unit

Explanation:

$Area = 2 \int_{0}^{a} y d x = 2 \int_{0}^{a} \sqrt{4 a x} d x$

$= 2 \times 2 \sqrt{a} \int_{0}^{a} \sqrt{x} d x$

$= 4 \sqrt{a} \times \frac{2}{3}$ $| x^{3 / 2} |_{0}^{a}$

$= \frac{8 \sqrt{a}}{3} (a^{3 / 2} - 0)$

$= \frac{8}{3} a^{2} sq. units.$

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