The arch of a bridge that spans a river is in the shape of an ellipse 70 feet wide. One arch support is located at each of the foci, 5 feet from each base of the ellipse.

Question

a) What is the maximum height of the arch?

b) How far from the center of the arch is it 10 feet high?

Answer 1

desmos.com/calculator/t2fhdzsiog

This graph on Desmos shows that the sum of the distances from any point on the ellipse to each of the foci is constant.

desmos.com/calculator/nkj1kkeg6t