Mathematics - Ellipse Question with Solution | TestHub

Let the ellipse ${\mathrm{E}}_1:\frac{x^2}{{\mathrm{a}}^2}+\frac{y^2}{{\mathrm{b}}^2}=1,\mathrm{a}>\mathrm{b}$ and ${\mathrm{E}}_2:\frac{x^2}{{\mathrm{A}}^2}+\frac{y^2}{{\mathrm{B}}^2}=1,\mathrm{A}<\mathrm{B}$ have same eccentricity $\frac{1}{\sqrt{3}}$. Let the product of their lengths of latus rectums be $\frac{32}{\sqrt{3}}$, and the distance between the foci of $E_1$ be 4. If $E_1$ and $E_2$ meet at $A,B,C$ and $D$, then the area of the quadrilateral $ABCD$ equals :