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

Let $\displaystyle \mathrm{e}_1$ and $\displaystyle \mathrm{e}_2$ be the eccentricities of the ellipse, $\displaystyle \frac{x^2}{25}+\frac{y^2}{\mathrm{~b}^2}=1(\mathrm{~b}<5)$ and the hyperbola, $\displaystyle \frac{x^2}{16}-\frac{y^2}{\mathrm{~b}^2}=1$ respectively satisfying $\displaystyle e_1 e_2=1$. If $\displaystyle \alpha$ and $\displaystyle \beta$ are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair $\displaystyle (\alpha, \beta)$ is equal to :