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Question

If the chord joining two points whose eccentric angles are α and β, cut the major axis of an ellipse at a distance c from the centre, then tanα2tanβ2=

A
c+aca
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B
cac+a
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C
aca+c
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D
a+cac
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Solution

The correct option is B cac+a
The equation of the chord joining points whose eccentric angle are α and β on the ellipse x2a2+y2b2=1, is xacos(α+β2)+ybsin(α+β2)=cos(αβ2)
This will cut the major axis at the point (c,0), if
cacos(α+β2)=cos(αβ2)
=cos(α+β2)cos(αβ2)=ac
cos(α+β2)+cos(αβ2)cos(α+β2)cos(αβ2)=a+cac
tanα2tanβ2=a+cac

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