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: