Question

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 1

`(x^2)/(36) + (y^2)/(100) = 1`

Explanation:

Required

The equation of the ellipse

This is calculated as:

`(x^2)/(a^2) + (y^2)/(b^2) = 1`

Where:

`b =6` ---- height

`a = 0.5 * 20 =10` --- width

So:

`(x^2)/(a^2) + (y^2)/(b^2) = 1`

`(x^2)/(6^2) + (y^2)/(10^2) = 1`

`(x^2)/(36) + (y^2)/(100) = 1`