The eccentricity of an ellipse E with centre at the origin O is (√ 3)/2 and its directrices are x= ± (4 √ 6)/3. Let H: x^2/(a^2)-y^2/(b^2)=1 be a…

The eccentricity of an ellipse E with centre at the origin O is $\displaystyle \frac{\sqrt{3}}{2}$ and its directrices are $\displaystyle x= \pm \frac{4 \sqrt{6}}{3}$. Let $\displaystyle \mathrm{H}: \frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{~b}^2}=1$ 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 :