Let the eccentricity of an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is reciprocal to that of the hyperbola $2x^{2} - 2y^{2} = 1$. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is $\_\_\_\_$.