Mathematics - Hyperbola Question with Solution | TestHub

Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E:\frac{(x-1{)}^2}{100}+\frac{(y-1{)}^2}{75}=1$ 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