The interactive picture below represents a straw, AD, that has been bent in half at point B. Drag point D and watch the straw flex itself. What kind of curve does point C and its reflection, point E, seem to trace?
Move point C to a new location. Clear the trace by clicking the red 'X' in the lower right corner. Drag point D again. How has your curve changed?
You can change the length of the straw by dragging either end of the red segment in the upper left corner.
How does the shape of the ellipse vary for different locations of point C?
What shape does point C trace when it lies directly on point B?
Suppose you wish to draw an ellipse with a 16-inch major axis and an 8-inch minor axis. How long a straw do you need, and where should you place point C?
Although you can't move point C off segment BD, imagine that it was placed somewhere on segment AB. What curve would it trace as you dragged point D?
Can you prove algebraically that point C traces an ellipse when it lies on BD?