A bridge is built in the shape of a semi elliptical arch. It has a span of 96 feet. The height of the arch 29 feet from the center is to be 10 feet. Find the height of the arch at its center.

Answer 1

the semi-axis along the base is 48, so we have

x^2/48^2 + y^2/b^2 = 1
The curve contains (29,10), so

29^2/48^2 + 10^2/b^2 = 1
b = 12.55

Answer 2

An archway that is above a highway is in the shape of semi ellipse 60ft wide and 25 ft high. How high is the archway 10 ft away from the center?