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Question

What is the eccentricity of a hyperbola if a chord joining 2 points given by parameters α and β also passes through the focus. [Given :α + β = p,α  β = q]



A

cos

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B

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C

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D

cos

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Solution

The correct option is B


we should do good if we know the chords equation joining 2 points of a hyperbola x2a2  y2b2 = 1

which is,

xa.cos[αβ2]  yb.sin.[α+β2] = cos[α+β2]

since this process through focus (ae,0)

e.cos[αβ2]  0 = cos[α+β2]

 e = cos[α+β2]cos[αβ2] = cosp2cosq2

Hence option (b)


Mathematics

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