...not to the discerning eye!
OK, put an hyperbola on a set of coordinate axes. Make it the kind that has a valley on top and a mountain below. However, do NOT center it at the origin. Move it up the y-axis a bit so that the x-axis chops off part of the mountain section.
The equation of this thing might be:
(y-k)<sup>2</sup>/b<sup>2</sup> - (x-0)<sup>2</sup>/a<sup>2</sup> = 1
This has three missing parameters. We had better have three significant pieces of information. Fortunately, we do!
There are three known points from your description:
(30,0), (-30,0), and (0,20)
Unfortunately, since the structure of the equation can't tell the difference between +30 and -30 for 'x', this does not lead to a unique solution. You get to pick the shape you want! What could be cooler? You may as well pick a simple one, but none will be all that easy.
Pick any 'k' greater than 20 and go from there.
b = k-20
'a' is a little trickier.
I had good results with k=40, b=20, and a=22.5 Of course, depending on what you are doing in this dome, that design may be entirely inadequate.
As for the last piece, once you have your equation, just plug in x = 25 and find the resulting y value that is LESS THAN 20. You will get two values and one of them will be greater than 20. Why?
You can have some fun with the design. This one wan't bad, either: k = 250, b = 230, a = 70.4297
