Parabolic mirrors: Reflector telescopes use parabolic mirrors because they have the shape that will reflect incoming light to a single point, the focal point (see Figure 3.72). The graph of y = x2 has...

Parabolic mirrors: Reflector telescopes use parabolic mirrors because they have the shape that will reflect incoming light to a single point, the focal point (see Figure 3.72). The graph of y = x2 has the shape of a parabola, for example. Light traveling vertically down (parallel to the y-axis) encounters the parabola and is reflected according to the law that the angle of incidence equals the angle of reflection. This law implies that vertical light rays encountering the parabola at a point (a, a2 ) will be reflected along the line

a. Find where the light rays reflected from the points (2, 4) and (3, 9) meet.

b. The point you found in part a is the focal point. Show that every vertical light ray that is reflected from the mirror passes through this point.