The length of latus rectum of the parabola whose focus is $\left(\frac{{\mathrm{u}}^2}{2\mathrm{g}}\mathrm{Sin}2\mathrm{\alpha },\frac{-{\mathrm{u}}^2}{2\mathrm{g}}\mathrm{Cos}2\mathrm{\alpha }\right)$ and directrix is $\mathrm{y}=\frac{{\mathrm{u}}^2}{2\mathrm{g}}$ is
 

Length of latus rectum=4a=2(2a)

$$\begin{gathered} =2(perpendicular \mathrm{distance} from \mathrm{focus} to \mathrm{directrix}) \\ =2\left(\frac{{\displaystyle \left|\frac{-{\mathrm{u}}^2}{2\mathrm{g}}\cos 2\mathrm{\alpha }-\frac{{\mathrm{u}}^2}{2\mathrm{g}}\right|}}{\sqrt{1}}\right) \\ =\frac{2{\mathrm{u}}^2}{\mathrm{g}}{\cos }^2\mathrm{\alpha } \end{gathered}$$