Question

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 height of the arch is 6 meters above the center of the river. Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch.

Answer 1

Title:

Check the explanation.

Step-by-step explanation:

The standard form of an ellipse is $\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1$.

The span of the river is 20 meters. As per the given condition, y-axis will pass through the middle point of the river. That is why, the value of a will be $\frac{20}{2} = 10$.

Since the height of the arc is 6, the value of b is 6.

The equation of the arc will become $\frac{x^2}{{10}^2} + \frac{y^2}{6^2} = 1$.