Conic Sections · Ellipse and hyperbola parameters

The eccentricity of an ellipse

E

with centre at the origin

O

\dfrac{\sqrt3}{2}

and its directrices are

x = \pm\dfrac{4\sqrt6}{3}

. Let

H : \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1

be a hyperbola whose eccentricity is equal to the length of semi-major axis of

E

, and whose length of latus rectum is equal to the length of minor axis of

E

. Then the distance between the foci of

H

is:

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