Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Need help with an ellipse problem?
A bridge is built in the shape of a semielliptical arch. It has a span of 98 feet. The height of the arch 30 feet from the center is to be 11 feet. Find the height of the arch at its center.
1 Answer
- Yves From CanadaLv 61 decade agoFavorite Answer
The equation of the ellipse is :
(x^2/a^2) + (y^2/b^2) = 1
We know that the span of the bridge is 98 feet. That means a = 98 / 2 = 49
The equation so far is :
(x^2/49^2) + (y^2/b^2) = 1
We know also that when x = 30 then y = 11. Just replace those values in the equation :
(30^2/49^2) + (11^2/b^2) = 1
We have to solve for b which is the height of the ellipse :
(30^2/49^2) + (11^2/b^2) = 1
(11^2/b^2) = 1 - (30^2/49^2)
b^2 = (11^2) / (1 - (30^2/49^2))
b = sqrt[(11^2) / (1 - (30^2/49^2))]
b = sqrt(193.5516)
b = 13.91 feet
