Coordinate Geometry: JEE Main 2020 Mathematics question

For some $\theta \in \left( {0,{\pi \over 2}} \right)$, if the eccentricity of the hyperbola, x²–y²sec²$\theta$ = 10 is $\sqrt 5$ times the eccentricity of the ellipse, x²sec²$\theta$ + y² = 5, then the length of the latus rectum of the ellipse, is :