Let be a point on the parabola with focus . Let be the
Chapter 3, Problem 3.800(choose chapter or problem)
Let be a point on the parabola with focus . Let be the angle between the parabola and the line segment , and let be the angle between the horizontal line and the parabola as in the figure. Prove that . (Thus, by a principle of geometrical optics, light from a source placed at will be reflected along a line parallel to the -axis. This explains why paraboloids, the surfaces obtained by rotating parabolas about their axes, are used as the shape of some automobile headlights and mirrors for telescopes.)
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