A bridge is built in the shape of a semielliptical arch. The bridge has a span of 120 ft and a maximum height of 25 ft. Find an equation for the ellipse and then find the height of the arch at distances of 10, 30, and 50 ft from the center.

Question

A bridge is built in the shape of a semielliptical arch.   The bridge has a span of 120 ft and a maximum height of 25 ft.  Find an equation for the ellipse and then find the height of the arch at distances of 10, 30, and 50 ft from the center.

anonymous · Answer

For the equation I got this:
$$(x^2/120^2)+(y^2/25^2)=1$$

anonymous · Answer

For 10 ft, would I substitute 50 for x?

alexwee123 · Answer

120 is the width of the whole bridge 
so divide that by 2

anonymous · Answer

right, So the radius is 60 ft. 

60-10=50, so I substitute for x correct?

alexwee123 · Answer

there is no radius for an ellipse

anonymous · Answer

ughhhh, I was thinking of it as half a circle

alexwee123 · Answer

here look at this site it explains ellipses much better than i can http://www.mathwarehouse.com/ellipse/equation-of-ellipse.php