Find the area of the parabola `y^2=4a x`bounded by its latus rectum.

Options

A. `2b^(3)//3` square units
B. `4b^(2)//3` square unit
C. `b^(2)` square unit
D. `8b^(2)//3` square unit

Answer

D

Explanation

Given equation `y^(2) = 4bx = 2int_(0)^(b) sqrt(4bx) dx`
`= 4sqrt(b) xx 2/3 [x^(3/2)]_(0)^(b) = (8sqrt(b))/(3)[b^(3/2) - 0]`
`:.` area of parabola bounded by its latus rectum
`= (8b^(2))/(3)` sq. units