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`

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`

Explanation

To find the length of the latus rectum of the parabola given the focus and directrix, we can follow these steps:

### Step 1: Identify the focus and directrix
The focus of the parabola is given as:
\[ F = \left(\frac{u^2}{2g} \sin 2\alpha, -\frac{u^2}{2g} \cos 2\alpha\right) \]
The directrix is given as:
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