In the interactive model below, both circles have their centers at the origin, point O. Segment OC is a radius of the larger circle, and point A is the intersection of the radius with the smaller circle. As you drag point C, notice that segments AB and BC remain parallel to the x- and y-axes, respectively. What kind of curve does point B seem to trace?
You can clear the trace by clicking on the red 'X' in the lower right corner. Try changing the size of the circles by dragging points D and E.
Describe how you could draw an ellipse with a 10-inch major axis and an 8-inch minor axis using this method.
Prove algebraically that this method produces ellipses.