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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
cosα+cosβcos(αβ)
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B
sinαsinβsin(αβ)
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C
cosαcosβcos(αβ)
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D
sinα+sinβsin(α+β)
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Solution

## The correct option is B sinα+sinβsin(α+β)The equation of a chord joining points having eccentric angles α and β is given byxacos(α+β2)+ybsin(α+β2)=cos(α−β2)If it passes through (ae,0) thenecos(α+β2)=cos(α−β2)⇒e=cos(α−β2)cos(α+β2)⇒2sin(α+β2)cos(α−β2)2sin(α+β2)cos(α+β2)=sinα+sinβsin(α+β)

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