Light, Camera, Hyperbola!

It’s relatively easy to photograph behavior that models a parabola – you can photograph the stream coming out of a water fountain, for example.

Ellipses aren’t so difficult to find either, especially semi-ellipses.

However, a visual representation of a hyperbola is a little tougher to find. Here’s photo I took of a flashlight against a wall. The flashlight’s cone of light is intersected by the vertical wall, and the upper half of a hyperbola is clearly visible!

I pasted the image into Geometer’s Sketchpad, and plotted three points. Using the points’ coordinates and a lot of substitution, I was able to come up with a function that matched the edge of light fairly closely:

Now we’ll have to see if my Precalculus students can do it!

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