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Model a Parabolic Dish

 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.  

y x x in x 16ths in
3 6.000 6 0
6 8.485 8 8
9 10.392 10 6
12 12.000 12 0

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