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NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Ellipse

NDA 2014 · Mathematics · Ellipse

What is the length of the latus rectum of the ellipse 25 x^2+16...

What is the length of the latus rectum of the ellipse 25x2+16y2=40025 x^2+16 y^2=400 ?

Options

  1. A252\frac{25}{2}
  2. B254\frac{25}{4}
  3. C165\frac{16}{5}
  4. D325\frac{32}{5}

Correct answer

D. 325\frac{32}{5}

Step-by-step solution

25x2400=16y2400=400400⇒x216+y225=1\frac{25 x^2}{400}=\frac{16 y^2}{400}=\frac{400}{400} \Rightarrow \frac{x^2}{16}+\frac{y^2}{25} \quad=1 Length of latus rectum of ellipse =2a2b=2×165=325=\frac{2 a^2}{b}=\frac{2 \times 16}{5}=\frac{32}{5}.
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