Question

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

Answer 1

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`