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

1. 4e 4 – 24e 2 + 27 = 0
2. 4e 4 – 24e 2 + 35 = 0
3. 4e 4 – 12e 2 – 27 = 0
4. 4e 4 + 8e 2 – 35 = 0

Correct answer: 4e 4 – 24e 2 + 35 = 0

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