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

1 Answer
Douglas K.
Nov 7, 2017

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 #(0,0)#, therefore, the equation of the parabola is:

#y = 1/(4f)x^2#

where #f# is vertical distance from the vertex to the focal point.

The cross-section of the 12 in diameter circle at the top of the reflector tells us that the x values are #+-6#, when #y = 4#. Substitute the point #(6,4)# into the equation:

#4 = 1/(4f)6^2 #

#f = 6^2/4^2#

#f = 2.25#

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

Related questions
See all questions in Linear, Exponential, and Quadratic Models
Impact of this question
10236 views around the world
You can reuse this answer
Creative Commons License