A bridge is built in the shape of a semielliptical arch. It has a span of 112 feet. The height of the arch 26 feet from the center is to be 12 feet. Find the height of the arch at its center.

Question

anonymous · Answer

Might be able to solve this one using standard form of ellipse equation:
$$\large (x-h)^2/a^2+(y-k)^2/b^2=1.$$

anonymous · Answer

which one is h and k and b and a I need some one to explain me that

anonymous · Answer

The way I'm thinking of it, if you put the center of the ellipse at (0,0), then h=k=0, so that simplifies things. If the span is 112 feet, then the semi-major axis in the x direction is 56, that would be 'a'
I think you have to use the given information to solve for 'b.'

anonymous · Answer

and c is?

anonymous · Answer

b^2= a^2 -c^2

anonymous · Answer

I wouldn't worry about that. I don't think that information is needed.

If you model the ellipse as 
$$\large \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$
With a=56 feet, and the point on the ellipse, (26,12) as (x,y) then if you solve that equation for b, that should be the answer you are looking for.
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anonymous · Answer

okay give me a second yo finish it

anonymous · Answer

13.55 ft

anonymous · Answer

?

anonymous · Answer

Oh, I haven't worked it out yet, gimme a sec to check it...