WBJEE · Maths · Ellipse
\(B\) is an extremity of the minor axis of an ellipse whose foci are \(S\) and \(S^{\prime} .\) If \(\angle S B S^{\prime}\) is a right angle, then the eccentricity of the ellipse is
- A \(\frac{1}{2}\)
- B \(\frac{1}{\sqrt{2}}\)
- C \(\frac{2}{3}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Slope of \(S B, m_{1}=\frac{b-0}{0-a e}=-\frac{b}{a e}\) and slope of \(S^{\prime} B, m_{2}=\frac{b-0}{0-(-a e)}=\frac{b}{a e}\) since, \(\angle S B S^{\prime}\) is a right angle. \(\therefore\) \[m_{1} m_{2}=-1\] \(\Rightarrow \quad \frac{-b}{a e} \times \frac{b}{a e}=-1\)…
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