The modifications of the Two-Pins-and-a-String Construction are as follows:

1. The length of the segment AB must be made shorter than the length of segment F1F2.

2. Point C should not lie between points A and B. By dragging point C to either side of points A and B, the intersection points of the two circles will trace a hyperbola.

Answers to questions.

A1. The closer the ratio F1F2 / AB is to 1, the sharper the bends in the hyperbola. As the ratio increases, the bends are less sharp.

A2. If the length of segment AB is greater than the length of segment F1F2, the model draws an ellipse.