Mathematics - Hyperbola Question with Solution | TestHub

Let $e_1$ and $e_2$ be the eccentricities of the ellipse $\frac{{\mathrm{x}}^2}{{\mathrm{b}}^2}+\frac{{\mathrm{y}}^2}{25}=1$ and the hyperbola $\frac{{\mathrm{x}}^2}{16}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$, respectively. If $\mathrm{b}<5$ and ${\mathrm{e}}_1{\mathrm{e}}_2=1$, 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 :