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)            \[\frac{2{{u}^{2}}}{g}{{\cos }^{2}}\alpha \]

Correct Answer: D

Solution :

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