Let the circle C touch the line x-y+1=0, have the centre on the positive x -axis, and cut off a chord of length 4/(√ 13) along the line -3 x+2 y=1.…

Let the circle C touch the line $\displaystyle x-y+1=0$, have the centre on the positive x -axis, and cut off a chord of length $\displaystyle \frac{4}{\sqrt{13}}$ along the line $\displaystyle -3 x+2 y=1$. Let H be the hyperbola $\displaystyle \frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1$, whose one of the foci is the centre of C and the length of the transverse axis is the diameter of C. Then $\displaystyle 2 \alpha^2+3 \beta^2$ is equal to $\displaystyle \_\_\_\_$