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The length of the latus rectum of the pa...

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

A

`(u^(2))/(g)cos^(2)alpha`

B

`(u^(2))/(g)cos2alpha`

C

`(2u^(2))/(g)cos2alpha`

D

`(2u^(2))/(g)cos^(2)alpha`

Text Solution

Verified by Experts

The correct Answer is:
D
(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`
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