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If the angle between the asymptotes of h...

If the angle between the asymptotes of hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` id `(pi)/(3)`, then the eccentnricity of conjugate hyperbola is _________.

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The correct Answer is:
2
Let e and e' be the eccentricities of given hyperbola and its conjugate, respectively.
Given that `2 tan^(-1)((b)/(a))=(pi)/(3)`
`rArr" "(b)/(a)=(1)/(sqrt3)`
So, `e^(2)=1+(1)/(3)=(4)/(3)`
`(1)/(e'^(2))+(1)/(e^(2))=1`
`rArr" "(1)/(e'^(2))=(1)/(4)rArre'=2`
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