A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x - y + 2 = 0$ and $y + 2 = 0$, respectively. If the locus of the point $P$, that divides the rod $AB$ internally in the ratio $2 : 1$ is $9 \left( x ^ { 2 } + \alpha y ^ { 2 } + \beta x y + \gamma x + 28 y \right) - 76 = 0$, then $\alpha - \beta - \gamma$ is equal to :\\
(1) 22\\
(2) 21\\
(3) 23\\
(4) 24