Theory and ExamplesThe reflective property of parabolas

Chapter 11, Problem 81E

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Problem        81E

Theory and Examples

The reflective property of parabolas The accompanying figure shows a typical point P(x0 , y0) on the parabola y2 = 4px.The line L is tangent to the parabola at P. The parabola’s focus lies at F( p, 0). The ray L' extending from P to the right is parallel to the x-axis. We show that light from F to P will be reflected out along by showing that Establish this equality by taking the following steps.

a. Show that

b. Show that

c. Use the identity

to show that

Since

This reflective property of parabolas is used in applications like car headlights, radio telescopes, and satellite TV dishes.