For some $\theta \in \left( 0 , \frac { \pi } { 2 } \right)$, if the eccentricity of the hyperbola, $x ^ { 2 } - y ^ { 2 } \sec ^ { 2 } \theta = 10$ is $\sqrt { 5 }$ times the eccentricity of the ellipse, $x ^ { 2 } \sec ^ { 2 } \theta + y ^ { 2 } = 5$, then the length of the latus rectum of the ellipse, is\\
(1) $2 \sqrt { 6 }$\\
(2) $\sqrt { 30 }$\\
(3) $\frac { 2 \sqrt { 5 } } { 3 }$\\
(4) $\frac { 4 \sqrt { 5 } } { 3 }$