Question

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. $\frac{2u^{2}}{g}\cos 2\alpha$
• D. $\frac{2u^{2}}{g}\sin^{2}\alpha$

Answer 1

Answer: (D)

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

Answer 2

Perpendicular distance from the focus

$\left( \frac{u^{2}}{2g}\sin 2\alpha,\frac{u^{2}}{2g}\cos 2\alpha \right)$to the directrix y = $\frac{u^{2}}{2g}$ is $\frac{u^{2}}{2g}$ - $\frac{u^{2}}{2g}\cos 2\alpha$ = $\frac{u^{2}}{g}$sin²α . ⇒ the latus rectum = $\frac{2u^{2}}{g}$sin²α .