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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Ellipse

BITSAT 2021 · Mathematics · Ellipse

The eccentricity of the ellipse whose major axis is three times the...

The eccentricity of the ellipse whose major axis is three times the minor axis is:

Options

  1. A23\frac{\sqrt{2}}{3}
  2. B32\frac{\sqrt{3}}{2}
  3. C223\frac{2 \sqrt{2}}{3}
  4. D23\frac{2}{\sqrt{3}}

Correct answer

C. 223\frac{2 \sqrt{2}}{3}

Step-by-step solution

Let a be the major axis and bb, the minor axis of the ellipse, then 3 minor axis = major axis. ⇒3b=a\Rightarrow 3 b=a Eccentricity is given by: b2=a2(1−e2)⇒b2=9b2(1−e2)⇒19=(1−e2)⇒e2=89⇒e=223\begin{array}{l} b^{2}=a^{2}\left(1-e^{2}\right) \\ \Rightarrow b^{2}=9 b^{2}\left(1-e^{2}\right) \\ \Rightarrow \frac{1}{9}=\left(1-e^{2}\right) \\ \Rightarrow e^{2}=\frac{8}{9} \\ \Rightarrow e=\frac{2 \sqrt{2}}{3} \end{array}
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