Let Psx1, y1d be a point on the parabola y 2 4px with
Chapter , Problem 22(choose chapter or problem)
Let Psx1, y1d be a point on the parabola y 2 4px with focus Fsp, 0d. Let be the angle between the parabola and the line segment FP, and let be the angle between the horizontal line y y1 and the parabola as in the figure. Prove that . (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.) 0 x y F(p, 0) P(, ) =4px y=
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