Question

Find the area of the region bounded by the parabola y² = 16x and its latus rectum.

Answer 1

Comparing y² = 16x with y² = 4ax, we get

4a = 16

∴ a = 4

∴ Focus is S(a, 0) = (4, 0)

For y² = 16x, y = `4sqrt(x)`

Required area = area of the region OBSAO

= 2[area of the region OSAO]

= `2int_0^4 y*dx`, where y = `4sqrt(x)`

= `2int_0^4 4sqrt(x)*dx`

= `8[(x^(3/2))/(3/2)]_0^4`

= `8[2/3(4)^(3/2) - 0]`

= `8[2/3(2^2)^(3/2)]`

= `(128)/(3)` sq. units