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Latus Rectum of Ellipse

If α and β ar...

Question

If $α$ and $β$ are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

A

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B

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C

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D

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Solution

The correct option is D
$e = \frac{cos (\frac{α - β}{2})}{cos (\frac{α + β}{2})} = \frac{sin α + sin β}{sin (α + β)}$

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