The area of the region bounded by the parabol | vedclass

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Question

(B) The equation of the parabola is $y^2 = 12x$. Comparing this with $y^2 = 4ax$,we get $4a = 12$,so $a = 3$.The latus rectum is the line $x = a = 3$.

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(B) The equation of the parabola is $y^2 = 12x$. Comparing this with $y^2 = 4ax$,we get $4a = 12$,so $a = 3$.The latus rectum is the line $x = a = 3$.The area bounded by the parabola and its latus rectum is given by $A = 2 \int_{0}^{a} y \, dx = 2 \int_{0}^{3} \sqrt{12x} \, dx$.$A = 2 	imes \sqrt{12} \int_{0}^{3} x^{1/2} \, dx = 2 	imes 2\sqrt{3} \left[ \frac{x^{3/2}}{3/2} ight]_{0}^{3}$.$A = 4\sqrt{3} 	imes \frac{2}{3} 	imes (3)^{3/2} = \frac{8\sqrt{3}}{3} 	imes 3\sqrt{3} = 8 	imes 3 = 24$ sq. units.

The area of the region bounded by the parabola $y^2 = 12x$ and its latus rectum is . . . . . . sq. units.

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