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