Here we investigate the reflection properties of ellipses and hyperbolas.

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 α = β. This shows that light aimed at a focus F₂ of a hyperbolic mirror is reflected toward the other focus F₁.

Transcribed Image Text:

F₁ F₁ y, 0 Bl F₂ P F₂ P x