Parabola (String and Optical Properties)

This video opens with a typical way of constructing a parabola given a focus and directrix: simply line up the directrix with the focus, and make a fold. Move to a different point on the directrix, and repeat the process until you have many tangent lines to your parabola.

The string property of a parabola is written on the blue paper: It's simply a fancy way of saying that if I pick any point on my parabola, the distance from that point to the focus will be the same distance from the point to the directrix.

**If you want to play around with this definition of a parabola, you can use this geogebra worksheet: http://ggbm.at/ERJhm75N **

This is a possible way to construct a parabola using that definition. You could have a class discussion/brainstorming session of why this method works/matches the string property.

Materials needed for construction: String, ruler, tape, marker, pin, corkboard.

Instructions:
1. Draw a line to be your directrix. Draw a point to be the focus. Measure the halfway point between the directrix and focus. Make a little mark.
2. Tape a string to your ruler, and pin the other end in the focus.
3. Start by looping your string until the bottom of the string is at the halfway point between the directrix and focus. Place your pen in this loop.
4. Keeping your ruler perpendicular to the directrix, gently slide it to the right, and keep your string tight next to the ruler.
5. To get the left half, flip the ruler over, and repeat the process.


To consider the special optical property associated with parabolas, you can try doing this geogebra activity: https://www.geogebra.org/o/ArkDus9h


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