Question

3. An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 6 meters above the center of the river. Write an equation for the ellipse if the x-axis coincides with the water level and the y-axis passes through the center of the arch.​

Answer 1

the equation for the ellipse that describes the arch is:

(x^2/20^2) + (y^2/6^2) = 1

Explanation:

An ellipse can be represented by the equation (x^2/a^2) + (y^2/b^2) = 1, where a and b are the lengths of the semi-major and semi-minor axes of the ellipse, respectively. In this case, the x-axis coincides with the water level and the y-axis passes through the center of the arch, so the center of the ellipse is at the point (0, 6).

For the arch in question, the semi-major axis is 20 meters (since the arch spans a river 20 meters wide) and the semi-minor axis is 6 meters (since the center of the arch is 6 meters above the center of the river).

So the equation for the ellipse that describes the arch is:

(x^2/20^2) + (y^2/6^2) = 1