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 \( 9 \left( x^2 + \alpha y^2 + \beta xy + \gamma x + 28y\right) - 76 = 0 \), then \( \alpha - \beta - \gamma \) is equal to