• # question_answer 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 A)            $\frac{{{u}^{2}}}{g}{{\cos }^{2}}\alpha$                                    B)            $\frac{{{u}^{2}}}{g}\cos 2\alpha$ C)            $\frac{2{{u}^{2}}}{g}{{\cos }^{2}}2\alpha$                                D)            $\frac{2{{u}^{2}}}{g}{{\cos }^{2}}\alpha$

According to the figure, the length of latus rectum is $2(SM)=2\times \frac{{{u}^{2}}}{2g}(1+\cos 2\alpha )=\frac{2{{u}^{2}}{{\cos }^{2}}\alpha }{g}$.