The length of the latus rectum of the parabola whose focus is a. `((u^2)/(2g)sin2alpha,-(u^2)/(2g)cos2alpha)` and directrix is `y=(u^2)/(2g)` is

Options

A. `(u^(2))/(g)cos^(2)alpha`
B. `(u^(2))/(g)cos2alpha`
C. `(2u^(2))/(g)cos2alpha`
D. `(2u^(2))/(g)cos^(2)alpha`

Answer

D

Explanation

(4) Length of latus rectum `=2xx` Distance of focus from directrix
`=2|(-(u^(2))/(2g)cos2alpha-(u^(2))/(2g))/(sqrt(1))|`
`=(2u^(2))/(g)cos^(2)alpha`