Let P(x1, y1) be a point on the parabola y2 = 4px with focus F(p, 0). Let a be the
Let P(x1, y1) be a point on the parabola y2 = 4px with focus F(p, 0). Let a be the angle between the parabola and the line segment FP, and let β be the angle between the horizontal line and the parabola as in the figure. Prove that a = β. (Thus, by a principle of geometrical optics, light from a source placed at F will be reflected along a line parallel to the x-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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