The length of the latus-rectum of the parabola whose focus is $\left(\frac{u^{2}}{2g} \sin 2\alpha,…
The length of the latus-rectum of the parabola whose focus is $\left(\frac{u^{2}}{2g} \sin 2\alpha, -\frac{u^{2}}{2g} \cos 2\alpha\right)$ and directrix is $y=\frac{u^{2}}{2g}$, is
\(\frac{u^2}{g} \cos ^2 \alpha\)
\(\frac{u^2}{g} \cos 2 \alpha\)
\(\frac{2 u^2}{g} \cos ^2 2 \alpha\)
\(\frac{2 u^2}{g} \cos ^2 \alpha\)
Solution
According to the figure, the length of latus rectum is
\(2(S M)=2 \times \frac{u^2}{2 g}(1+\cos 2 \alpha)=\frac{2 u^2 \cos ^2 \alpha}{g} .\)
