Parabola - Folding Activity
Latest update to this document: 26 February 2003

**Materials:**

- One rectangular piece of wax paper. Make sure edges are cut as neat and straight as possible
- Rulers

**Hands on Activity:**

- Mark bottom edge of paper with solid color (black)
- Make a dot (point F) 1"above the center of the lower edge of the paper.
- Fold the black line up so that it touches the dot. Make a sharp crease. Open the paper flat.
- Fold again in a different direction. Again make sure the black line touches the dot. Crease and
open flat.
- Repeat about 20 times, folding the paper in a different direction each time. The black line
must
**always** touch the dot.
- Lightly trace the curve that appears.
- This curve is called a parabola.

**Definition** - A parabola is the set of all points in a plane equidistant from a fixed point
(called the focus) and a fixed line (called the directrix). (The directrix is the black line)
- Mark a random point on the parabola (point B), using the ruler draw a line from that point B
to point F. Label the line K.
- Fold paper again so that the crease of the paper goes through point B while the edge of the
paper touches point F. You should see line K through wax paper, trace the line. Label it, line
L. This should form a perpendicular line with the lower edge of the paper
through point B.
- Unfold the paper, you can see line segments L and K are the same length. (Thus proving that the
distance from the focus to the point is equidistant to the distance from the point to the directrix.

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