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AP EAMCET · Maths · Ellipse

If \(S\) and \(S^{\prime}\) are the foci of an ellipse, \(B\) is one end of the minor axis and \(\angle S B S^{\prime}=90^{\circ}\), then the eccentricity of that ellipse is

  1. A \(\frac{\sqrt{3}}{2}\)
  2. B \(\frac{\sqrt{7}}{4}\)
  3. C \(\frac{1}{\sqrt{2}}\)
  4. D \(\frac{1}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{\sqrt{2}}\)

Step-by-step Solution

Detailed explanation

\(S\) and \(S^1\) are the foci of an ellipse \(\therefore\) Coordinate of foci \(=( \pm a e, 0)\) Slope of \(S B=\frac{b}{a e}\) Slope of \(S^1 B=\frac{-b}{a e}\) Now, \(\angle S B S^{\prime}=90\) So, slope of \(S B \times\) slope of \(S^{\prime} B=-1\)…