PS

We deliberately chose values of 6 cm and 8 cm for the lengths of AB to take advantage of the Pythagorean triple 3, 4, 5, so as to keep the numbers simple.

Thus the height of the ellipse is 8 cm (ie 2x4 cm) when AB = 6 cm and 6 cm (ie 2x3 cm) when AB = 8 cm.

When AB = 8 cm, the area of the ellipse is 3/4 of the area when AB = 6 cm (since the height is 3/4 of the 'original' height, and the width is unchanged).
In absolute terms, the area (in 1 cm squares) of the ellipse is 20pi when AB = 6 cm and 15pi when AB = 8 cm.

[A nice way of thinking about this is to see the area of an ellipse as pi/4 (ie about three quarters) of the area of the smallest enclosing rectangle.]

It may seem that we have restricted ourselves to two very special cases. However, we can still sense general properties of the ellipse: for example, the width is always 10 cm (the length of the string) and the height decreases as AB increases (from 5 cm to 0 cm as AB goes from 0 cm to 10 cm).

The end