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Ellipse Focal Reflection


Let C be a point on the ellipse with foci A and B and consider the line tangent to the ellipse at C. Let F be some point on the tangent other than C. Then AC + CB = AG + GB < AF + FB. Thus the shortest route from A to B that first touches the tangent line is the path that meets the tangent line at C. And as we've seen for such a path, the angle of incidence must equal the angle of reflection.