Question

A bridge is built in the shape of a semielliptical arch. It has a span of 112 feet. The height of the arch 26 feet from the center is to be 12 feet. Find the height of the arch at its center.

Answer 1

Solve this using standard form of ellipse equation: (x−h)^2/a^2+(y−k)^2/b^2=1.

Put the center of the ellipse at (0,0), then h=k=0, so that simplifies things. If the span is 112 feet, then the semi-major axis in the x direction is 56, that would be 'a' I think you have to use the given information to solve for 'b.'

Getting 13.5488, so 13.5 or 13.55 feet seems fine as a rounded answer.