# Tractrix (Pursuit Curve)

- Author:
- Tim Brzezinski

The applet below shows a

**brown boat**in the water. A**blue rope of fixed length**(that's always held taught) connects the**brown boat**to a**red point**. This**red point**stays on the**gray dock**and is allowed to move vertically along the dock. Go ahead and drag the**red point**upwards and observe the path traced out by the the**brown boat**. Feel free to do this for different values of taught rope length (adjustable by the blue slider.) After interacting with this applet for a few minutes, please answer the questions that appear below it.1) The tractrix is also called a

*curve of pursuit*. Can you explain, from your observations, why this label makes sense? 2) Suppose point P (the boat) has coordinates (x, y). Suppose the red point*A*has coordinates (0,a). Write an expression for the slope of the blue rope (segment*AP*) in the applet above. 3) Solve the differential equation you wrote for (2) above.