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.
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.
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Formula for the perimeter of a parabolic dish at
EFunda Area and Perimeter of a Parabola