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The blue line is a parabola with focus at the red dot. The axis of symmetry is the x-axis in this case.
Reflection Property for Parabolas: any particle that travels parallel to the axis of symmetry will reflect off the parabola and pass through the focus.
This reflection property makes parabolas useful to focus sound, which is why you see parabolic microphones on the sidelines of sporting events. These microphones use a paraboloid dish, which is created by rotating a paraboloid about its axis of symmetry. These process is also used to create flashlights by placing the light source at the focus, resulting in light rays that are parallel leaving the flashlight, giving the best beam.
Nice Animation (it may take awhile to load) that allows you to vary the incoming line (change the location of the point R) and see that the line always intersects the focus. This clearly shows that the importance of the angle of incidence being equal to the angle of reflection!