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