Question

Please Help! A bridge support is represented by the top half of an​ ellipse, shown in the figure to the right. The point​ Q, which is the center of the​ ellipse, is at the origin. The bridge support is 18 feet high at its center and it is 25 feet from either end of the bridge to the center. Find the equation that best describes the ellipse.

Answer 1

The elliptical arc of the bridge is described by the length of the given semi-major and semi minor axis.

• $\mathrm{The \ equation \ that \ best \ describes \ the \ ellipse \ is; }\ \displaystyle \underline{\frac{x^2}{25^2} + \frac{y^2}{18^2} = 1}$

Reasons:

The given parameters of the ellipse are;

Shape of the bridge support = Top half of the ellipse

Height of the bridge support at the center = 18 feet

Distance from the bridge support from the center on either side = 25 feet

The general equation of an ellipse is presented as follows;

$\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$

Where;

a = The semi major axis = The distance from the center to the left or right support  = 25 feet

b = The semi minor axis = The height of the ellipse at the center = 18 feet

Which gives;

$\displaystyle \mathrm{ \underline{The \ equation \ of \ the \ ellipse \ is; \ \frac{x^2}{25^2} + \frac{y^2}{18^2} = 1}}$

Learn more here:

https://brainly.com/question/4471526