Let P(x1, y1) be a point on the hyperbola x2/a2 y2/b2 = 1 with foci F1 and

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Let P(x1, y1) be a point on the hyperbola x2/a2 €“ y2/b2 = 1 with foci F1 and F2 and let α and β be the angles between the lines PF1, PF2 and the hyperbola as shown in the figure. Prove that a = β. (This is the reflection property of the hyperbola. It shows that light aimed at a focus F2 of a hyperbolic mirror is reflected toward the other focus F1.

F2 F, F;

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