SOLUTION: The arch of a bridge forms the upper half of an ellipse. The arch is 6 meters above the 20-meter-wide river. Write an equation for the ellipse in which its major axis coincides wit

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The arch of a bridge forms the upper half of an ellipse. The arch is 6 meters above the 20-meter-wide river. Write an equation for the ellipse in which its major axis coincides wit      Log On


   

Question 1165021: The arch of a bridge forms the upper half of an ellipse. The arch is 6 meters above the 20-meter-wide river. Write an equation for the ellipse in which its major axis coincides with the water level.
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Let the origin be at water level, halfway between the two ends of the bridge.

The major axis is 20 meters, so the semi-major axis is 10.

The height of the arch is 6 meters, so the semi-minor axis is 6.

Plug the numbers into the standard form of the equation for an ellipse:

x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2+=+1

x%5E2%2F10%5E2%2By%5E2%2F6%5E2+=+1

x%5E2%2F100%2By%5E2%2F36+=+1