The area of the region bounded by the parabol | vedclass

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(A) The equation of the parabola is $y^2 = 4ax$,where $4a = 4$,so $a = 1$. The focus of the parabola is $(a, 0) = (1, 0)$. The latus rectum is the lin

Vedclass · Accepted Answer

$\frac{8}{3}$

Vedclass · Answer

(A) The equation of the parabola is $y^2 = 4ax$,where $4a = 4$,so $a = 1$. The focus of the parabola is $(a, 0) = (1, 0)$. The latus rectum is the line $x = 1$. The area bounded by the parabola and the latus rectum is given by $A = 2 \int_{0}^{1} y \, dx$. Since $y^2 = 4x$,we have $y = 2\sqrt{x}$. $A = 2 \int_{0}^{1} 2\sqrt{x} \, dx = 4 \int_{0}^{1} x^{1/2} \, dx$. $A = 4 \left[ \frac{x^{3/2}}{3/2} ight]_{0}^{1} = 4 	imes \frac{2}{3} [x^{3/2}]_{0}^{1}$. $A = \frac{8}{3} [1 - 0] = \frac{8}{3}$ sq. units.

The area of the region bounded by the parabola $y^2 = 4x$ and its latus rectum is . . . . . . sq. units.

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