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If a directrix of a hyperbola centred at the origin and passing through the point `(4,-2 sqrt(3)) " is " 5x=4sqrt(5)` and its eccentricity is e, then

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The correct Answer is:
7

`16/a^(2) -12/b^(2)=1`
`16/a^(2) -12/(a^(2)(e^(2)-1))=1`
`16(e^(2)-1) -12 =a^(2)(e^(2)-1)`, since `a/e =4/sqrt(5)`
`16e^(2) - 16-12 = 16/5 e^(2)(e^(2)-1)`
`80e^(2) - 80 - 60 = 16(e^(4) - e^(2))`
`16e^(4) - 96e^(2) + 140=0`
`4e^(2) - 24e^(2) + 35=0`
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