Unformatted text preview: boloid of revolution as depicted below. 7.3 Parabolas 413 Every cross section through the vertex of the paraboloid is a parabola with the same focus. To see
why this is important, imagine the dashed lines below as electromagnetic waves heading towards
a parabolic dish. It turns out that the waves reﬂect oﬀ the parabola and concentrate at the focus
which then becomes the optimal place for the receiver. If, on the other hand, we imagine the dashed
lines as emanating from the focus, we see that the waves are reﬂected oﬀ the parabola in a coherent
fashion as in the case in a ﬂashlight. Here, the bulb is placed at the focus and the light rays are
reﬂected oﬀ a parabolic mirror to give directional light. F Example 7.3.5. A satellite dish is to be constructed in the shape of a paraboloid of revolution. If
the receiver placed at the focus is located 2 ft above the vertex of the dish, and the dish is to be
12 feet wide, how deep will the dish be?
Solution. One way to approach this problem...
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