Question

The “Hatch Shell” in Boston has the arch with semi-elliptical form with a horizontal major axis. The base of the arch is 110-foot long and the highest part of the arch is 40 feet above the scene. Find the height of the arch of the “Hatch Shell” 33 feet away from the midpoint of the base of the arch.

Answer 1

Draw a diagram, with the center of the base at (0,0)

It is easy to see that the equation of the ellipse is

x^2/55^2 + y^2/40^2 = 1

Now just find y when x=33