Let $e _ { 1 }$ and $e _ { 2 }$ be the eccentricities of the ellipse $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( b < 5 )$ and the hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ respectively satisfying $\mathrm { e } _ { 1 } \mathrm { e } _ { 2 } = 1$. If $\alpha$ and $\beta$ are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair $( \alpha , \beta )$ is equal to:
(1) $( 8,10 )$
(2) $\left( \frac { 20 } { 3 } , 12 \right)$
(3) $( 8,12 )$
(4) $\left( \frac { 24 } { 5 } , 10 \right)$