Let E_1: x^2/(a^2)+y^2/(b^2)=1, a > b. Let E_2 be another ellipse such that it touches the end points of major axis of E_1 and the foci of E_2 are…

Let $\displaystyle \mathrm{E}_1: \frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1, \mathrm{a}>\mathrm{b}$. Let $\displaystyle \mathrm{E}_2$ be another ellipse such that it touches the end points of major axis of $\displaystyle \mathrm{E}_1$ and the foci of $\displaystyle \mathrm{E}_2$ are the end points of minor axis of $\displaystyle \mathrm{E}_1$. If $\displaystyle \mathrm{E}_1$ and $\displaystyle \mathrm{E}_2$ have same eccentricities, then its value is :