Let the foci of a hyperbola H coincide with the foci of the ellipse E: ((x-1)^2)/100+((y-1)^2)/75=1 and the eccentricity of the hyperbola H be the…

Let the foci of a hyperbola $\displaystyle H$ 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 $\displaystyle H$ be the reciprocal of the eccentricity of the ellipse $\displaystyle E$. If the length of the transverse axis of $\displaystyle H$ is $\displaystyle \alpha$ and the length of its conjugate axis is $\displaystyle \beta$, then $\displaystyle 3 \alpha^2+2 \beta^2$ is equal to