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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Ellipse

NDA 2012 · Mathematics · Ellipse

If the latus rectum of an ellipse is equal to half of the minor...

If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity?

Options

  1. A2/32 / \sqrt{3}
  2. B1/31 / \sqrt{3}
  3. C3/2\sqrt{3} / 2
  4. D1/21 / \sqrt{2}

Correct answer

C. 3/2\sqrt{3} / 2

Step-by-step solution

2b2a=b2b=ab2=a2(1−e2)b2=4b2(1−e2)14=1−e2e2=1−14=34e=32.\begin{aligned} \frac{2 b^2}{a} & =b \\ 2 b & =a \\ b^2 & =a^2\left(1-e^2\right) \\ b^2 & =4 b^2\left(1-e^2\right) \\ \frac{1}{4} & =1-e^2 \\ e^2 & =1-\frac{1}{4}=\frac{3}{4} \\ e & =\frac{\sqrt{3}}{2}.\end{aligned}
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