WBJEE · Maths · Ellipse
The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is \(90^{\circ}\). The eccentricity of the ellipse is
- A \(\frac{1}{8}\)
- B \(\frac{1}{\sqrt{3}}\)
- C \(\sqrt{\frac{2}{3}}\)
- D \(\sqrt{\frac{1}{2}}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{\frac{1}{2}}\)
Step-by-step Solution
Detailed explanation
\( \begin{gathered} \text { } \frac{b}{a e}=\tan \frac{\pi}{4} \\ \qquad \begin{array}{c} a e \Rightarrow \frac{b}{a}=e \\ e^2=1-\frac{b^2}{a^2} \\ e^2=1-e^2 \end{array} \end{gathered} \)\( e^2=\frac{1}{2} \Rightarrow e=\frac{1}{\sqrt{2}} \)
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