Let A(0, a+2), B(0, a), C(-2,0) and D(2,0) be four points and the lines A D and B C intersect at P(x, y). If the locus of P is the curve f(x, y )=0…

Let $\displaystyle A(0, a+2), B(0, a), C(-2,0)$ and $\displaystyle D(2,0)$ be four points and the lines $\displaystyle A D$ and $\displaystyle B C$ intersect at $\displaystyle P(x, y)$. If the locus of $\displaystyle P$ is the curve $\displaystyle f(x, \mathrm{y})=0$ and the tangent at the point $\displaystyle (4, \gamma)$ on this curve is $\displaystyle \frac{x}{\alpha}+\frac{y}{\beta}=1$, then $\displaystyle \alpha(\beta-\gamma)$ is equal to \_\_\_\_.