Let the foci of a hyperbola \( H \) coincide with the foci of the ellipse \(\displaystyle E:\ \frac{(x-1)^{2}}{100}+\frac{(y-1)^{2}}{75}=1 \) and the eccentricity of the hyperbola \( H \) be the reciprocal of the eccentricity of the ellipse \( E \). If the length of the transverse axis of \( H \) is \( \alpha \) and the length of its conjugate axis is \( \beta \), then \( 3\alpha^{2}+2\beta^{2} \) is equal to
