JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is
- A \(\frac{{2\sqrt 2 - 1}}{2}\)
- B \(\sqrt 2 - 1\)
- C \(\frac{1}{2}\)
- D \(\frac{{\sqrt 2 - 1}}{2}\)
Answer & Solution
Correct Answer
(B) \(\sqrt 2 - 1\)
Step-by-step Solution
Detailed explanation
Focus of an ellipse is given as \(\left( { \pm ae,0} \right)\) distance between then \(=2ae\) According to the quation, \(2ae = \frac{{{b^2}}}{a}\) \( \Rightarrow 2{a^2}e = {b^2} = {a^2}\left( {1 - {e^2}} \right)\)…
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