Conic Sections Question 47
Question: The length of the latus-rectum of the parabola whose focus is $ ( \frac{u^{2}}{2g}\sin 2\alpha ,\ -\frac{u^{2}}{2g}\cos 2\alpha ) $ and directrix is $ y=\frac{u^{2}}{2g} $ , is
Options:
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 $
Show Answer
Answer:
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{2u^{2}{{\cos }^{2}}\alpha }{g} $ .
BETA
