It is extremely difficult to calculate the shape of sheets for a parabolic dish, but it is easy to calculate a form. A step form for a parabolic dish would consist of a rising series of shrinking circles.
The basic equation for a parabola is x^2 = py. For total y height and x radius, p = x^2 / y.
For every three to six inch interval for y, x = sqrt(py). The diameter of each rising, shrinking circle is 2x. For a parabolic dish of 24 inches wide & 12 inches high, p = (24/2)^2 / 12 = 12.
|y||p*y||√ p*y = x||x inches||(fraction of inch) * 16
appx= 16ths in
|3||36||6.000||6||0 / 16|
|6||72||8.485||8||8 / 16|
|9||108||10.392||10||6 / 16|
|12||144||12.000||12||0 / 16|
Formula for the perimeter of a parabolic dish at
EFunda Area and Perimeter of a Parabola