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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Ellipse

NDA 2012 · Mathematics · Ellipse

What is the eccentricity of the conic 4 x^2+9 y^2=144 ?

What is the eccentricity of the conic 4x2+9y2=1444 x^2+9 y^2=144 ?

Options

  1. A53\frac{\sqrt{5}}{3}
  2. B54\frac{\sqrt{5}}{4}
  3. C35\frac{3}{\sqrt{5}}
  4. D2/32 / 3

Correct answer

A. 53\frac{\sqrt{5}}{3}

Step-by-step solution

x226+y216=1a2=36,62=16\frac{x^2}{26}+\frac{y^2}{16}=1 \quad a^2=36,6^2=16 we have, b2=a2(1−c2)b^2=a^2\left(1-c^2\right)1636=1−e21−e2=49(A)1−49=e259=e2⇒e=53.\begin{aligned} \frac{16}{36} & =1-e^2 \\ 1-e^2 & =\frac{4}{9}(\mathrm{ A}) \\ 1-\frac{4}{9} & =e^2 \quad \frac{5}{9}=e^2 \Rightarrow e=\frac{\sqrt{5}}{3}. \end{aligned}$$
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