If I start plugging in the formula as written to an excel spreadsheet, several of the results for 1561.78-27.7483*x^2 are negative. Even after adding the 39.154 the square root will fail. Perhaps it is your order of operations.
I couldn't resist playing with this. Is it also possible that your conic value should be -.2517? That way -27.7483 would just be -.7483 and the curve would look like this:
Also, you might make your sketch from 0 to 11 so that you can revolve the curve about the center axis.
I have been thinking about this some more. I don't sleep much....
I am more familiar with the conic formula in the form: y(x) = (x^2/R)/(1+(1-(1+(K))*(x/R)^2)^.5)
It is a formula for a Rho variable driven conic curve where X determines the start and end points; K is the Rho variable where 0 = circle, 0 > K > -1 = ellipse, -1 = parabolic, and K < -1 is hyperbolic; R is the radius of curvature. To expand this for even coefficeints it would be: y(x) = (x^2/R)/(1+(1-(1+(K))*(x/R)^2)^.5) + Dx^2 + Dx^4...Another thing you might consider is that a revolved surface will be less accurate than a boundary surface when used as an optical reference surface. This a thread where the topic was discussed a while ago: https://forum.solidworks.com/message/157294#157294Harold