HELP Really difficult calculus project

[don1231915]

HELP! Really difficult calculus project!

Homework Statement

OK, SO I have a upside down parabola structure with the specifications as follows:
The building has a rectangular base 150m long and 72m wide. The maximum height should not exceed 75% of its width or be less than half the width and the min. height of a room in a public building is 2.5m

The question is:

How do I create the curved roof structure (parabola? or hyperbole? or ellipse?) when the height is 36m??
How do I find the equation of the curve whether it is a parabola? or ½ ellipse? using the data above? Which curve would be the best one to use?

The Attempt at a Solution

If I use a parabola, I came up with an equation y=-0.03x^2+36 but that seems completely wrong as I have no idea how I reached to -0.03. I just used trial and error to get a nice looking curve.

PLS HELP!

 

[HallsofIvy]

I don't understand what you are asking here. You say, initially "parabola structure" but then ask whether it is a parabola or ellipse? Are we to assume that the curved top (whether parabola or ellipse) spans the 72 m width or 150 meter length?

Assuming this is a "parabolic cylinder with with the parabola crossing the smaller 72 m width, then we want the height to be between 1/2(72)= 36 m and (3/4)72= 54 m. A parabola that passes through (-36, 0) and (36, 0) and has height h is of the form \(\displaystyle y= h(1296- x^2)/1296\). h can be any number between 36 and 54.

 

[don1231915]

It could be anything, but I decided it to be an ellipse
So,
(x^2/a^2)+(y^2/b^2) = 1 is the equation

and then would a and b be both 36? if I want the height to be 36m??

So, the equation is
x^2+y^2=1296
So when graphing, would the equation be just y= sqrt (1296-x^2)?
That gived a decent graph btw

PLease give me your feedback on this

Also, can you explain me again the equation of the parabola
what is [/math] ,I didnt really understand that whole equation

and yes, the h is between 36 and 54, that's kinda obvious from the question

Thank you so much!