Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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The Eccentricity of the Ellipse, If the Minor Axis is Equal to the Distance Between the Foci, is - Mathematics

MCQ
Short Note
Sum

The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci, is

Options

  • \[\frac{\sqrt{3}}{2}\]

     

  • \[\frac{2}{\sqrt{3}}\]

     

  • \[\frac{1}{\sqrt{2}}\]

     

  • \[\frac{\sqrt{2}}{3}\]

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Solution

\[\frac{1}{\sqrt{2}}\]
According to the question, the minor axis is equal to the distance between the foci.
\[i . e . 2b = 2ae\]
\[ \Rightarrow e = \frac{b}{a} . . . (1) \]
\[\text{ Now,} e = \sqrt{1 - \frac{b^2}{a^2}}\]
\[ \Rightarrow e = \sqrt{1 - e^2} [From (1)] \]
On squaring both sides, we get:
\[ e^2 = 1 - e^2 \]
\[ \Rightarrow 2 e^2 = 1\]
\[ \Rightarrow e^2 = \frac{1}{2}\]
\[ \Rightarrow e = \frac{1}{\sqrt{2}}\]

Concept: Introduction of Ellipse
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Q 6 | Page 28
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