Let $e _ { 1 }$ be the eccentricity of the hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ and $e _ { 2 }$ be the eccentricity of the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 , a > b$, which passes through the foci of the hyperbola. If $e _ { 1 } e _ { 2 } = 1$, then the length of the chord of the ellipse parallel to the x -axis and passing through $( 0,2 )$ is: (1) $4 \sqrt { 5 }$ (2) $\frac { 8 \sqrt { 5 } } { 3 }$ (3) $\frac { 10 \sqrt { 5 } } { 3 }$ (4) $3 \sqrt { 5 }$
Let $e _ { 1 }$ be the eccentricity of the hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ and $e _ { 2 }$ be the eccentricity of the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 , a > b$, which passes through the foci of the hyperbola. If $e _ { 1 } e _ { 2 } = 1$, then the length of the chord of the ellipse parallel to the x -axis and passing through $( 0,2 )$ is:\\
(1) $4 \sqrt { 5 }$\\
(2) $\frac { 8 \sqrt { 5 } } { 3 }$\\
(3) $\frac { 10 \sqrt { 5 } } { 3 }$\\
(4) $3 \sqrt { 5 }$