Hyperbola

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