Let \({e}_{1}\) and \({e}_{2}\) be the eccentricities of the ellipse \(\frac{{x}^{2}}{{b}^{2}}+\frac{{y}^{2}}{25}=1\) an…

Let \({e}_{1}\) and \({e}_{2}\) be the eccentricities of the ellipse \(\frac{{x}^{2}}{{b}^{2}}+\frac{{y}^{2}}{25}=1\) and the hyperbola \(\frac{{x}^{2}}{16}-\frac{{y}^{2}}{{b}^{2}}=1\), 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 :

[JEE Main 2025, 7 Apr (Shift 2)]