# Find the area of the region bounded by the parabola y^2 = 4ax and its latus rectum. - Mathematics and Statistics

Find the area of the region bounded by the parabola y2 = 4ax and its latus rectum.

#### Solution

Given equation of parabola is y2 = 4ax

y=2sqrtasqrtx

Required area = Area of region OBSAO = 2(area of region OSAO)

=2int_0^aydx

=2int_0^a2sqrtasqrtx

=4sqrtaint_0^asqrtxdx

=4sqrta[2/3x^(3/2)]_0^a

=8/3 sqrta[a^(3/2)]

therefore A=8/3a^2 sq.units

Concept: Area of the Region Bounded by a Curve and a Line
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