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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Ellipse

JEE Main · Mathematics · Ellipse

The angle between the lines joining the foci of an ellipse to one...

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is 90∘90^{{}^{{}^{\circ}}}. The eccentricity of the ellipse isThe angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is 90^ ^ ^ .

Options

  1. A18\frac{1}{8}
  2. B13\frac{1}{\sqrt{3}}
  3. C23\sqrt{\frac{2}{3}}
  4. D12\sqrt{\frac{1}{2}}

Correct answer

D. 12\sqrt{\frac{1}{2}}

Step-by-step solution

\begin{gathered}\frac{b}{a e}=\tan \frac{\pi}{4}\\ \qquad ae⇒ba=ee2=1−b2a2e2=1−e2\begin{array}{c}a e \Rightarrow \frac{b}{a}=e \\ e²=1-\frac{b^2}{a^2}\\ e²=1-e² \end{array} \end{gathered} e²=12⇒\frac{1}{2} \Rightarrowe=12\frac{1}{\sqrt{2}}The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is 90^ ^ ^ .
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