If a directrix of a hyperbola centered at the origin and passing through the point \( (4,-2 \sqr....

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If a directrix of a hyperbola centered at the origin and passing through the point \( (4,-2 \sqrt{3}) \) is \( 5 x=4 \sqrt{5} \)
\( \mathrm{P} \)
and its eccentricity is \( e \), then
(1) \( 4 e^{4}-12 e^{2}-27=0 \)
(2) \( 4 e^{4}-24 e^{2}+27=0 \)
(3) \( 4 e^{4}+8 e^{2}-35=0 \)
(4) \( 4 e^{4}-24 e^{2}+35=0 \)


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