If ${\mathrm{e}}_1$ and ${\mathrm{e}}_2$ are the eccentricities of $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ and $\frac{{\mathrm{x}}^2}{{\mathrm{b}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{a}}^2}=1$respectively  then

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