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Question 11

The eccentricity of an ellipse E with centre at the origin O is $$\dfrac{\sqrt{3}}{2}$$ and its directrices are $$x = \pm \dfrac{4\sqrt{6}}{3}$$. 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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