Painter on a ladder

The problem: Line AB is a ladder leaning on a vertical wall. A (risk-taking) painter (P) is standing on the ladder mid-way. The ladder starts slipping down the wall (and across the floor) due to the painter's weight. What will be the path (or curve) of the painter standing at the mid-point, as the ladder slides all the way down? Explore: 1. Click on the "Show mid-point" check-box to see the painter (point P) 2. Click-and-drag point A down, to see the ladder slipping 3. Watch point P as you move point A up and down, and get a sense for the curve or path that point P makes on the plain. 4. You can visualize the path by right-clicking on the point P and selecting "Trace On" from the popup menu (to turn tracing off, right-click on P again, and de-select "Trace On") Can you guess what kind of path point P is tracing? 5. For a hint, click on the "Show hint" check-box, and move point A up and down to observe the behavior of line segment b (connecting point E to P). 6. To see more details to help you figure out the path of point P, click on the "Show more details" check-box. Observe the various shapes that are formed as they change while you move point A up and down. 7. You can click on the "Show path" check-box to see the path of point P. Formalize your observations by capturing the path of P in algebraic form.