The length of the latus-rectum of the parabola whose focus is \(\left(\frac{u^2}{2 g} \sin 2 \alpha,-\frac{u^2}{2 g} \cos 2 \alpha\right)\) and directrix is \(y=\frac{u^2}{2 g}\), is

• A

  \(\frac{u^2}{g} \cos ^2 \alpha\)
• B

  \(\frac{u^2}{g} \cos 2 \alpha\)
• C

  \(\frac{2 u^2}{g} \cos ^2 2 \alpha\)
• Correct answer
  D

  \(\frac{2 u^2}{g} \cos ^2 \alpha\)

Solution

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

Hence, the correct answer is option: 'D'.