Let $ P(x_1, y_1) $ be a point on the hyperbola $ x^2/a^2 - y^2/b^2 = 1 $ with foci $ F_1 $ and $ F_2 $ and let $ \alpha $ and $ \beta $ be the angles between the lines $ PF_1 $, $ PF_2 $ and the hyperbola as shown in the figure. Prove that $ \alpha = \beta $. (This is the reflection property of the hyperbola. It shows that light aimed at a focus $ F_2 $ of a hyperbolic mirror is reflected toward the other focus $ F_1 $.)