# Evolute of a Tractrix

- Author:
- Tim Brzezinski

- Topic:
- Straight Lines

Shown below is a

**tractrix (pursuit curve)**and a**BIG GRAY POINT**that lies on it. The reflection of this point about the x-axis is also shown (as a much smaller gray point).**The pink lines**are normal to the tractrix. (Recall that a**normal line**to a curve at a point is the line that is perpendicular to the line tangent to the curve at that point.) Drag the**BIG GRAY POINT**along this**tractrix**and observe this envelope of normal lines (i.e. the traces of the**pink lines**). As you do, be sure to keep your finger pressed down on your mouse button as you get closer and closer to the x-axis. (Otherwise, the**GRAY POINT**will disappear and you'll have to refresh the page or adjust the slider a bit.) What do you see? How do your results compare with that from this worksheet? https://tube.geogebra.org/m/FasSGc84