How to delete cases of complex numbers with a four point parabola?

Questions
1

I am working on using the function FourPointParabola created by Ed Pegg Jr on the Function Repository.

FourPointParabolas /@ RandomChoice[Range[2, 100, 2], {3, 4, 2}]

I have the following output and I want to delete the cases with imaginary numbers:

{{(15 (1157603 + 33640 Sqrt[1155]))/(4 (30 + Sqrt[1155])^2) - (
   45 (4425 + 116 Sqrt[1155]) \[FormalX])/(4 (30 + Sqrt[1155])^2) - (
   15 (12700 + 377 Sqrt[1155]) \[FormalY])/(30 + Sqrt[
     1155])^2 + (-((135 \[FormalX])/(
      272 (-(45/34) - (3 Sqrt[1155])/68))) + \[FormalY])^2, (
   3174811 + 21732 Sqrt[1155])/1156 - (
   3 (70305 + 1808 Sqrt[1155]) \[FormalX])/1156 + 
   1/289 (1840 + 
      849 Sqrt[
       1155]) \[FormalY] + ((-(45/34) - (3 Sqrt[1155])/
        68) \[FormalX] + \[FormalY])^2}, {-((
    120 I (-65047423 I + 70608 Sqrt[354765]))/(-1097 I + Sqrt[
      354765])^2) + (
   2 (277636987 + 71352 I Sqrt[354765]) \[FormalX])/(-1097 I + Sqrt[
     354765])^2 + (
   4 (46953508 + 91563 I Sqrt[354765]) \[FormalY])/(-1097 I + Sqrt[
     354765])^2 + ((2659 \[FormalX])/(
     586 (1097/586 + (I Sqrt[354765])/586)) + \[FormalY])^2, (
   60 (7790366 + 5855 I Sqrt[354765]))/85849 - (
   I (-20589854 I + 38795 Sqrt[354765]) \[FormalX])/85849 - (
   2 I (-7857911 I + 1790 Sqrt[354765]) \[FormalY])/
   85849 + ((1097/586 + (I Sqrt[354765])/
        586) \[FormalX] + \[FormalY])^2}, {(
   684 (11932079 + 7064 Sqrt[2851026]))/(1710 + Sqrt[2851026])^2 + (
   684 (6365 + 4 Sqrt[2851026]) \[FormalX])/(1710 + Sqrt[
     2851026])^2 - (
   228 (2098399 + 1243 Sqrt[2851026]) \[FormalY])/(1710 + Sqrt[
     2851026])^2 + ((57 \[FormalX])/(
     1282 (-(855/641) - Sqrt[1425513/2]/641)) + \[FormalY])^2, (
   6 (277760141 + 107194 Sqrt[2851026]))/410881 - (
   6 (19678585 + 11686 Sqrt[2851026]) \[FormalX])/410881 + (
   2 (11964599 + 17167 Sqrt[2851026]) \[FormalY])/
   410881 + ((-(855/641) - Sqrt[1425513/2]/
        641) \[FormalX] + \[FormalY])^2}}

How can I delete the terms with complex coefficients?

2

By “delete the terms” I assume you mean terms at the first level. So, if I call your data stuff, then at the start stuff has three terms. You can select the terms that don’t contain any complex numbers.

Select[stuff, FreeQ[_Complex]]

Caveat: I’m not familiar with FourPointParabolas, and I don’t know if I’ve interpreted your question correctly.

3

I found a working solution.

Select[FreeQ[_Complex]][{{Rational[
     15, 4] (30 + 1155^Rational[1, 2])^(-2) (
     1157603 + 33640 1155^Rational[1, 2]) + Rational[-45, 4] (
      30 + 1155^Rational[1, 2])^(-2) (
     4425 + 116 1155^Rational[1, 2]) \[FormalX] - 15 (
     30 + 1155^Rational[1, 2])^(-2) (
    12700 + 377 1155^Rational[1, 2]) \[FormalY] + (
     Rational[-135, 272] (
        Rational[-45, 34] + Rational[-3, 68]
           1155^Rational[1, 2])^(-1) \[FormalX] + \[FormalY])^2, 
   Rational[1, 1156] (
     3174811 + 21732 1155^Rational[1, 2]) + Rational[-3, 1156] (
     70305 + 1808 1155^Rational[1, 2]) \[FormalX] + Rational[1, 289] (
     1840 + 849 1155^Rational[1, 2]) \[FormalY] + ((
       Rational[-45, 34] + Rational[-3, 68]
          1155^Rational[1, 2]) \[FormalX] + \[FormalY])^2}, {Complex[
     0, -120] (Complex[0, -1097] + 354765^Rational[1, 2])^(-2) (
     Complex[0, -65047423] + 70608 354765^Rational[1, 2]) + 2 (
     277636987 + Complex[0, 71352] 354765^Rational[1, 2]) (
      Complex[0, -1097] + 354765^Rational[1, 2])^(-2) \[FormalX] + 4 (
     46953508 + Complex[0, 91563] 354765^Rational[1, 2]) (
      Complex[0, -1097] + 354765^Rational[1, 2])^(-2) \[FormalY] + (
     Rational[2659, 586] (Rational[1097, 586] + Complex[0, 
Rational[1, 586]]
           354765^Rational[1, 2])^(-1) \[FormalX] + \[FormalY])^2, 
   Rational[60, 85849] (
     7790366 + Complex[0, 5855] 354765^Rational[1, 2]) + Complex[0, 
Rational[-1, 85849]] (
     Complex[0, -20589854] + 38795 354765^Rational[
        1, 2]) \[FormalX] + Complex[0, 
Rational[-2, 85849]] (
     Complex[0, -7857911] + 1790 354765^Rational[
        1, 2]) \[FormalY] + ((Rational[1097, 586] + Complex[0, 
Rational[1, 586]]
          354765^Rational[1, 2]) \[FormalX] + \[FormalY])^2}, {684 (
      1710 + 2851026^Rational[1, 2])^(-2) (
     11932079 + 7064 2851026^Rational[1, 2]) + 684 (
      1710 + 2851026^Rational[1, 2])^(-2) (
     6365 + 4 2851026^Rational[1, 2]) \[FormalX] - 228 (
     1710 + 2851026^Rational[1, 2])^(-2) (
    2098399 + 1243 2851026^Rational[1, 2]) \[FormalY] + (
     Rational[
       57, 1282] (
        Rational[-855, 641] + Rational[-1, 641]
           Rational[1425513, 2]^Rational[
           1, 2])^(-1) \[FormalX] + \[FormalY])^2, 
   Rational[6, 410881] (
     277760141 + 107194 2851026^Rational[1, 2]) + Rational[-6, 
      410881] (19678585 + 11686 2851026^Rational[
        1, 2]) \[FormalX] + Rational[2, 410881] (
     11964599 + 17167 2851026^Rational[1, 2]) \[FormalY] + ((
       Rational[-855, 641] + Rational[-1, 641]
          Rational[1425513, 2]^Rational[
          1, 2]) \[FormalX] + \[FormalY])^2}}]