Exploring ellipse shapes

Topic:
Ellipse
This applet allows you to explore how the transverse diameter (sum of distances from point on ellipse to the foci) and the distance between the foci affect the shape of the ellipse (e.g., very elongated, close to a circle, etc.). You can drag any of the points A, B, C in order to change the shape of the ellipse. Use this to answer the questions under the applet.
In the applet above, a, b, and d denote the lengths of the three segments shown. You can see these values changing as you drag the A, B, C points. 1. In what ways are points A and B different from point C, in terms of their relationship to the ellipse? List at leasts two ways in which they are different. 2. By dragging any of the points A, B, C, try to make the ellipse look almost like a circle. Write a sentence about the relationship among a, b, and d that makes this happen. 3. By dragging any of the points A, B, C, try to make the ellipse look almost like a segment. Write a sentence about the relationship among a, b, and d that makes this happen. 4. Make a conjecture regarding how the relationship among a, b and d affects the shape of the ellipse, in general.