Puzzles

The area of an ellipse is \(\pi ab\) where \(a\) and \(b\) are the distances from the centre of the ellipse to the closest and furthest points on the ellipse.

In the first ellipse, \(a=5\mathrm{cm}\) and \(b=4\mathrm{cm}\), so the area is \(20\pi\mathrm{cm}^2\). In the second ellipse, \(a=5\mathrm{cm}\) and \(b=3\mathrm{cm}\), so the area is \(15\pi\mathrm{cm}^2\). Hence, the first ellipse has the larger area.

How far apart should the pins be placed to give the ellipse with the largest area?