Chapter 11.3, Problem 52E

To determine

To state:why the boundary of the lighted area is a hyperbola and how can one hold a flashlight to forms a hyperbola on the ground.

Answer to Problem 52E

The light from the source is generally blocked off to produce a cone of light, and then that cone is intersected with the wall, creating a conic section. For typical arrangements of light fixtures, that section is generally a hyperbola.

on a angle of grater than ${45}^{\circ }$ .

Explanation of Solution

Given information:

From the figure provided in the question it is observed that the boundary of the lighted area is a hyperbola.

The light from the source is generally blocked off to produce a cone of light, and then that cone is intersected with the wall, creating a conic section. For typical arrangements of light fixtures, that section is generally a hyperbola.

To forms a hyperbola on the ground, the flashlight must be hold on a angle of grater than ${45}^{\circ }$ .