# A parabolic flashlight reflector is to be 12 inches across and 4 inches deep. Where should the lightbulb be placed?

##### 1 Answer

Nov 7, 2017

#### Answer:

The bulb should be placed in the center of the reflector at a point 2.25 inches up from the bottom of the reflector.

#### Explanation:

The cross-section of the parabolic reflector forms a parabola.

Let the vertex of the parabola be the point

where

The cross-section of the 12 in diameter circle at the top of the reflector tells us that the x values are

The bulb should be placed in the center of the reflector at a point 2.25 inches up from the bottom of the reflector.