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 :
