Question

The length of the latus-rectum of the parabola whose focus is $\left( \frac{u^{2}}{2g}\sin 2\alpha,\mspace{6mu} - \frac{u^{2}}{2g}\cos 2\alpha \right)$ 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. $\frac{2u^{2}}{g}\cos^{2}2\alpha$
• D. $\frac{2u^{2}}{g}\cos^{2}\alpha$

Answer 1

Answer: (D)

$\frac{2u^{2}}{g}\cos^{2}\alpha$

Answer 2

According to the figure, the length of latus rectum is 2(SM) = 2 x $\frac{u^{2}}{2g}(1 + \cos 2\alpha)\mspace{6mu} = \mspace{6mu}\frac{2u^{2}\cos^{2}\alpha}{g}$