Grade 11 Precalculus

Question

The arch of a bridge is in the shape of a semi-ellipse, with its major axis at the water level. Suppose the arch is 40 ft high in the middle, and 160 ft across its major axis. How high above the wa ter level is the arch, at a point 30 ft from the center (horizontally)?

Answer 1

Again, you need a labelled sketch and the standard equation of an ellipse. It will be easiest if you make the origin the center of the ellipse.

Now, the equation is x²/a² + y²/b² = 1 where a is half the major axis (80) and b is half the minor axis (40):

x²/80² + y²/40² = 1

Plug in x = 30

y = 37.1