Let e_1 and e_2 be the eccentricities of the ellipse x^2/(b^2)+y^2/25=1 and the hyperbola x^2/16-y^2/(b^2)=1, respectively. If b <5 and e_1 e_2=1,…

Let $\displaystyle \mathrm{e}_1$ and $\displaystyle \mathrm{e}_2$ be the eccentricities of the ellipse $\displaystyle \frac{x^2}{\mathrm{~b}^2}+\frac{y^2}{25}=1$ and the hyperbola $\displaystyle \frac{x^2}{16}-\frac{y^2}{\mathrm{~b}^2}=1$, respectively. If $\displaystyle \mathrm{b}<5$ and $\displaystyle \mathrm{e}_1 \mathrm{e}_2=1$, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is :