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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Ellipse

NDA 2013 · Mathematics · Ellipse

The length of latus rectum of the ellipse 4 x^2+9 y^2=36 is

The length of latus rectum of the ellipse 4x2+9y2=364 x^2+9 y^2=36 is

Options

  1. A43\frac{4}{3}
  2. B83\frac{8}{3}
  3. C6
  4. D12

Correct answer

B. 83\frac{8}{3}

Step-by-step solution

Standard equation of ellipse is: x2a2+y2b2=1Length\frac{x^2}{a^2}+\frac{y^2}{b^2}=1Length of latus rectum =2b2aGivenequationis\frac{2 b^2}{a} Given equation is4 x^2+9 y^2=36or,or,x29+y24=1a2=9,b2=4\begin{aligned} \frac{x^2}{9}+\frac{y^2}{4}& =1 \\ a^2 & =9, b^2=4 \end{aligned}LengthofLength oflatus rectum =\frac{2 \times 4}{3}=\frac{8}{3}$
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