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BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Mathematics
Chapter
Parabola

BITSAT 2011 · Mathematics · Parabola

The length of the latus-rectum of the parabola whose focus is...

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}), isThe length of the latus-rectum of the parabola whose focus is (((u^2)/(2 g) 2 α,-(u^2)/(2 g) 2 α)) and directrix is

Options

  1. A(\frac{u^2}{g} \cos ^2 \alpha)
  2. B(\frac{u^2}{g} \cos 2 \alpha)
  3. C(\frac{2 u^2}{g} \cos ^2 2 \alpha)
  4. D(\frac{2 u^2}{g} \cos ^2 \alpha)

Correct answer

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

Step-by-step 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} .) The length of the latus-rectum of the parabola whose focus is (((u^2)/(2 g) 2 α,-(u^2)/(2 g) 2 α)) and directrix is
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