>    test_for_conic := proc(n) local m, L, C, i, poss_comb, j, f, b1, b2, b3, b4, b5, solns, g, solnsa, h, solnsb, val;

>    m := evalf(n);

>    L := [[trunc(m*10) mod 10, trunc(m*100) mod 10], [trunc(m*100) mod 10, trunc(m*1000) mod 10], [trunc(m*1000) mod 10, trunc(m*10000) mod 10], [trunc(m*10000) mod 10, trunc(m*100000) mod 10], [trunc(m*100000) mod 10, trunc(m*1000000) mod 10], [trunc(m*1000000) mod 10, trunc(m*10) mod 10]];

>    C := [c1, c2, c3, c4, c5, c6];

>    for i to 6 do geometry:-point(C[i], op(L[i])) end do;

>    poss_comb := combinat:-choose(C, 3);

>    for j to nops(poss_comb) do if geometry:-AreCollinear(op(poss_comb[j])) = true then RETURN(n, "vacuously true") end if; end do;

>    f := (x, y) -> x^2 + 2*a1*x*y + a2*y^2 + a3*x + a4*y + a5;

>    b1 := f(op(L[1]));

>    b2 := f(op(L[2]));

>    b3 := f(op(L[3]));

>    b4 := f(op(L[4]));

>    b5 := f(op(L[5]));

>    solns := solve({b1, b2, b3, b4, b5});

>    if solns = NULL then g := (x, y) -> a0*x^2 + 2*a1*x*y + y^2 + a3*x + a4*y + a5; b1 := g(op(L[1])); b2 := g(op(L[2])); b3 := g(op(L[3])); b4 := g(op(L[4])); b5 := g(op(L[5])); solnsa := solve({b1, b2, b3, b4, b5}); if solnsa = NULL then h := (x, y) -> 2*a1*x*y + a3*x + a4*y + a5; b1 := h(op(L[1])); b2 := h(op(L[2])); b3 := h(op(L[3])); b4 := h(op(L[4])); b5 := h(op(L[5])); solnsb := solve({b1, b2, b3, b4, b5}); val := eval(h(op(L[6])), solnsb) end if; val := eval(g(op(L[6])), solnsa) end if;

>    if solns <> NULL then val := eval(f(op(L[6])), solns) end if;

>    if val = 0 then RETURN(n, eval(f(x, y), solns)) else RETURN(n, false) end if;

>    end proc:

Warning, this will take a long, long, long time to execute.  I've broken the calculation into thirds as Maple had difficulty trying to display the whole thing (it would freeze).  Each piece takes about 1.5 hours on my computer.

>    ans := []: for k from 666667/999999 to 999999/999999 by 1/999999 do z := test_for_conic(k); if z[2] <> false and z[2] <> "vacuously true" then ans := [op(ans), [z]] end if end do: nops(ans);

7506

>    for alpha to nops(ans) do ans[alpha] end do;

[6010/9009, x^2+2/5*x*y-1/6*y^2-42/5*x-7/30*y+37/5]

[6011/9009, x^2+1/2*x*y-1/5*y^2-10*x-2/5*y+78/5]

[31775/47619, x^2+3*x*y+1/2*y^2-29*x-49/2*y+159]

[668/1001, x^2+2/3*x*y-1/4*y^2-12*x-3/4*y+51/2]

[74149/111111, x^2+6/5*x*y-1/5*y^2-71/5*x-23/5*y+204/5]

[859/1287, x^2+x*y-1/3*y^2-15*x-5/3*y+40]

[6014/9009, x^2+2*x*y-1/2*y^2-22*x-11/2*y+75]

[547/819, x^2-x*y+y^2-7*x-7*y+48]

[2006/3003, x^2-2/3*x*y+1/2*y^2-10*x-5/2*y+45]

[860/1287, x^2+x*y-1/3*y^2-12*x-4/3*y+20]

[669/1001, x^2+4/3*x*y-2/5*y^2-15*x-12/5*y+174/5]

[6022/9009, x^2+2*x*y-1/2*y^2-20*x-5*y+60]

[6023/9009, x^2+4*x*y-2/3*y^2-33*x-44/3*y+130]

[6025/9009, x^2-4*x*y-2*y^2+13*x+52*y-210]

[287/429, x^2-4/3*x*y+2*y^2-5*x-20*y+90]

[670/1001, x^2+2*x*y-1/2*y^2-18*x-9/2*y+45]

[6031/9009, x^2+3*x*y-3/5*y^2-25*x-9*y+408/5]

[464/693, x^2+6*x*y-3/4*y^2-44*x-99/4*y+375/2]

[862/1287, x^2-6*x*y-3/2*y^2+26*x+117/2*y-273]

[6035/9009, x^2-3*x*y-3*y^2+7*x+63*y-240]

[6037/9009, x^2+2/7*x*y+y^2-8*x-8*y+7]

[670207/999999, x^2+3/7*x*y+y^2-9*x-9*y+14]

[6038/9009, x^2+109/76*x*y+113/38*y^2-261/19*x-561/19*y+896/19]

[60937/90909, x^2+4/7*x*y+y^2-10*x-10*y+21]

[61/91, x^2+134/9*x*y+47/3*y^2-76*x-208*y+483]

[223469/333333, x^2+5/7*x*y+y^2-11*x-11*y+28]

[670507/999999, x^2+6/7*x*y+y^2-12*x-12*y+35]

[95801/142857, x^2+x*y+y^2-13*x-13*y+42]

[223570/333333, x^2+2/7*x*y+1/6*y^2-8*x-13/6*y+7]

[670760/999999, x^2+x*y+y^2-13*x-13*y+42]

[670762/999999, x^2+3*x*y+y^2-27*x-27*y+140]

[670763/999999, x^2+4*x*y+y^2-34*x-34*y+189]

[223588/333333, x^2+5*x*y+y^2-41*x-41*y+238]

[670765/999999, x^2+6*x*y+y^2-48*x-48*y+287]

[95824/142857, x^2+9*x*y+y^2-69*x-69*y+434]

[60979/90909, x^2+10*x*y+y^2-76*x-76*y+483]

[670807/999999, x^2+9/7*x*y+y^2-15*x-15*y+56]

[670907/999999, x^2+10/7*x*y+y^2-16*x-16*y+63]

[671017/999999, x^2+6+y^2-7*x-7*y]

[223687/333333, x^2+12/5*x*y-6*y^2-77/5*x+168/5*y+72/5]

[223690/333333, x^2+2/7*x*y+1/6*y^2-8*x-13/6*y+7]

[6046/9009, x^2+2/5*x*y-1/6*y^2-42/5*x-7/30*y+37/5]

[6047/9009, x^2+1/3*x*y+y^2-28/3*x-28/3*y+67/3]

[671317/999999, x^2+1/2*x*y+y^2-21/2*x-21/2*y+61/2]

[96/143, x^2+76/41*x*y+131/41*y^2-711/41*x-1521/41*y+3826/41]

[671417/999999, x^2+2/3*x*y+y^2-35/3*x-35/3*y+116/3]

[6049/9009, x^2+63/2*x*y+26*y^2-335/2*x-835/2*y+2589/2]

[323/481, x^2+5/6*x*y+y^2-77/6*x-77/6*y+281/6]

[223870/333333, x^2+12/5*x*y-6*y^2-77/5*x+168/5*y+72/5]

[671617/999999, x^2+x*y+y^2-14*x-14*y+55]

[223907/333333, x^2+1/3*x*y+1/5*y^2-28/3*x-44/15*y+251/15]

[24880/37037, x^2+6+y^2-7*x-7*y]

[671761/999999, x^2+x*y+y^2-14*x-14*y+55]

[223921/333333, x^2+3*x*y+y^2-28*x-28*y+153]

[671764/999999, x^2+4*x*y+y^2-35*x-35*y+202]

[671765/999999, x^2+5*x*y+y^2-42*x-42*y+251]

[671768/999999, x^2+8*x*y+y^2-63*x-63*y+398]

[10663/15873, x^2+9*x*y+y^2-70*x-70*y+447]

[223939/333333, x^2+4/3*x*y+y^2-49/3*x-49/3*y+214/3]

[671917/999999, x^2+3/2*x*y+y^2-35/2*x-35/2*y+159/2]

[224009/333333, x^2-1/5*x*y+y^2-33/5*x-33/5*y+46/5]

[865/1287, x^2+38/17*x*y-43/17*y^2-252/17*x+168/17*y+235/17]

[672127/999999, x^2+19+y^2-8*x-8*y]

[224054/333333, x^2+5/2*x*y-5*y^2-18*x+30*y+2]

[224057/333333, x^2+1/3*x*y+1/5*y^2-28/3*x-44/15*y+251/15]

[6056/9009, x^2+1/2*x*y-1/5*y^2-10*x-2/5*y+78/5]

[673/1001, x^2+2/5*x*y+y^2-54/5*x-54/5*y+193/5]

[96061/142857, x^2+3/5*x*y+y^2-61/5*x-61/5*y+242/5]

[466/693, x^2+49/19*x*y+67/19*y^2-435/19*x-915/19*y+2990/19]

[672515/999999, x^2+5*x*y-3*y^2-28*x-4*y+97]

[672527/999999, x^2+4/5*x*y+y^2-68/5*x-68/5*y+291/5]

[6059/9009, x^2+62*x*y+37*y^2-352*x-748*y+2895]

[224207/333333, x^2+5/2*x*y-5*y^2-18*x+30*y+2]

[224209/333333, x^2+x*y+y^2-15*x-15*y+68]

[24916/37037, x^2+2/5*x*y+1/4*y^2-54/5*x-81/20*y+281/10]

[32036/47619, x^2+3*x*y+1/2*y^2-29*x-49/2*y+159]

[61160/90909, x^2-x*y+y^2-x-y-30]

[672761/999999, x^2+19+y^2-8*x-8*y]

[224254/333333, x^2+x*y+y^2-15*x-15*y+68]

[672764/999999, x^2+3*x*y+y^2-29*x-29*y+166]

[224255/333333, x^2+4*x*y+y^2-36*x-36*y+215]

[74752/111111, x^2+7*x*y+y^2-57*x-57*y+362]

[672769/999999, x^2+8*x*y+y^2-64*x-64*y+411]

[672827/999999, x^2+7/5*x*y+y^2-89/5*x-89/5*y+438/5]

[224309/333333, x^2+8/5*x*y+y^2-96/5*x-96/5*y+487/5]

[673037/999999, x^2-1/2*x*y+y^2-11/2*x-11/2*y+15/2]

[24931/37037, x^2-1/4*x*y+y^2-29/4*x-29/4*y+79/4]

[6065/9009, x^2+49/13*x*y-47/13*y^2-300/13*x+180/13*y+317/13]

[673237/999999, x^2+32+y^2-9*x-9*y]

[74807/111111, x^2+8/3*x*y-4*y^2-21*x+24*y+6]

[24936/37037, x^2+2/5*x*y+1/4*y^2-54/5*x-81/20*y+281/10]

[674/1001, x^2+2/3*x*y-1/4*y^2-12*x-3/4*y+51/2]

[74824/111111, x^2+6/5*x*y-1/5*y^2-71/5*x-23/5*y+204/5]

[6067/9009, x^2+1/2*x*y+y^2-25/2*x-25/2*y+113/2]

[32069/47619, x^2-6*x*y-5*y^2+17*x+89*y-264]

[673537/999999, x^2+3/4*x*y+y^2-57/4*x-57/4*y+275/4]

[74848/111111, x^2+8/3*x*y-4*y^2-21*x+24*y+6]

[673637/999999, x^2+x*y+y^2-16*x-16*y+81]

[289/429, x^2+73/3*x*y+9*y^2-158*x-254*y+1227]

[6805/10101, x^2+29/3*x*y+y^2-66*x-74*y+423]

[32083/47619, x^2+1/2*x*y+1/3*y^2-25/2*x-35/6*y+85/2]

[673760/999999, x^2-2*x*y+y^2+5*x+5*y-66]

[20417/30303, x^2-x*y+y^2-2*x-2*y-17]

[673762/999999, x^2+32+y^2-9*x-9*y]

[673763/999999, x^2+x*y+y^2-16*x-16*y+81]

[673765/999999, x^2+3*x*y+y^2-30*x-30*y+179]

[673768/999999, x^2+6*x*y+y^2-51*x-51*y+326]

[673769/999999, x^2+7*x*y+y^2-58*x-58*y+375]

[673837/999999, x^2+3/2*x*y+y^2-39/2*x-39/2*y+211/2]

[61267/90909, x^2+7/4*x*y+y^2-85/4*x-85/4*y+471/4]

[61277/90909, x^2-x*y+y^2-3*x-3*y-4]

[6073/9009, x^2-18/13*x*y+17/13*y^2-28/13*x-56/13*y+15/13]

[20428/30303, x^2-4/3*x*y+y^2-11/3*x-5/3*y+14/3]

[674147/999999, x^2-2/3*x*y+y^2-16/3*x-16/3*y+37/3]

[6074/9009, x^2-61/24*x*y+9/4*y^2+13/6*x-47/6*y+7/3]

[32107/47619, x^2-1/3*x*y+y^2-23/3*x-23/3*y+86/3]

[675/1001, x^2+14*x*y-11*y^2-72*x+36*y+95]

[674347/999999, x^2+45+y^2-10*x-10*y]

[224788/333333, x^2+3*x*y-3*y^2-25*x+15*y+30]

[32113/47619, x^2+1/2*x*y+1/3*y^2-25/2*x-35/6*y+85/2]

[868/1287, x^2+x*y-1/3*y^2-15*x-5/3*y+40]

[6077/9009, x^2+2/3*x*y+y^2-44/3*x-44/3*y+233/3]

[224881/333333, x^2+3*x*y-3*y^2-25*x+15*y+30]

[674647/999999, x^2+x*y+y^2-17*x-17*y+94]

[2026/3003, x^2+13/2*x*y+4*y^2-51*x-87*y+410]

[6815/10101, x^2+8*x*y+y^2-57*x-63*y+362]

[224899/333333, x^2-4*x*y-2/3*y^2+13*x+104/3*y-156]

[224918/333333, x^2+2/3*x*y+1/2*y^2-44/3*x-55/6*y+191/3]

[224920/333333, x^2-3*x*y+y^2+11*x+11*y-102]

[674761/999999, x^2-2*x*y+y^2+4*x+4*y-53]

[61342/90909, x^2-x*y+y^2-3*x-3*y-4]

[224921/333333, x^2+45+y^2-10*x-10*y]

[674764/999999, x^2+x*y+y^2-17*x-17*y+94]

[674768/999999, x^2+5*x*y+y^2-45*x-45*y+290]

[6079/9009, x^2+6*x*y+y^2-52*x-52*y+339]

[74983/111111, x^2+5/3*x*y+y^2-65/3*x-65/3*y+380/3]

[225019/333333, x^2-2*x*y+y^2+3*x+3*y-40]

[6082/9009, x^2-19/26*x*y+89/104*y^2-231/52*x-357/104*y+179/52]

[96451/142857, x^2-3/2*x*y+y^2-1/2*x-1/2*y-31/2]

[675203/999999, x^2-7/5*x*y+23/20*y^2-17/10*x-13/4*y-3/5]

[79/117, x^2-x*y+y^2-4*x-4*y+9]

[61387/90909, x^2-x*y+y^2-4*x-4*y+9]

[52/77, x^2-28/17*x*y+23/17*y^2-27/17*x-81/17*y+166/17]

[225119/333333, x^2-1/2*x*y+y^2-15/2*x-15/2*y+67/2]

[6085/9009, x^2-13/2*x*y+4*y^2+45/2*x-15/2*y-83/2]

[675457/999999, x^2+58+y^2-11*x-11*y]

[32165/47619, x^2+4*x*y-2*y^2-33*x+92]

[225158/333333, x^2+2/3*x*y+1/2*y^2-44/3*x-55/6*y+191/3]

[6086/9009, x^2+2*x*y-1/2*y^2-22*x-11/2*y+75]

[32174/47619, x^2+4*x*y-2*y^2-33*x+92]

[2029/3003, x^2+x*y+y^2-18*x-18*y+107]

[225229/333333, x^2-2*x*y-1/2*y^2-64+39/2*y]

[675760/999999, x^2-4*x*y+y^2+17*x+17*y-138]

[675761/999999, x^2-3*x*y+y^2+10*x+10*y-89]

[225254/333333, x^2-2*x*y+y^2+3*x+3*y-40]

[61433/90909, x^2-x*y+y^2-4*x-4*y+9]

[675764/999999, x^2+58+y^2-11*x-11*y]

[75085/111111, x^2+x*y+y^2-18*x-18*y+107]

[6088/9009, x^2+4*x*y+y^2-39*x-39*y+254]

[675769/999999, x^2+5*x*y+y^2-46*x-46*y+303]

[6089/9009, x^2+13/8*x*y+1/4*y^2-203/8*x-119/8*y+1119/8]

[676010/999999, x^2+6+y^2-7*x-7*y]

[225340/333333, x^2+1/6*x*y+y^2-8*x-8*y+12]

[676030/999999, x^2+1/3*x*y+y^2-9*x-9*y+18]

[676040/999999, x^2+1/2*x*y+y^2-10*x-10*y+24]

[225350/333333, x^2+2/3*x*y+y^2-11*x-11*y+30]

[676070/999999, x^2+x*y+y^2-13*x-13*y+42]

[25040/37037, x^2+7/6*x*y+y^2-14*x-14*y+48]

[676090/999999, x^2+4/3*x*y+y^2-15*x-15*y+54]

[6091/9009, x^2-2/5*x*y+y^2-28/5*x-28/5*y+23/5]

[676121/999999, x^2+19+y^2-8*x-8*y]

[225377/333333, x^2+1/5*x*y+y^2-46/5*x-46/5*y+131/5]

[676141/999999, x^2+2/5*x*y+y^2-52/5*x-52/5*y+167/5]

[96593/142857, x^2+3/5*x*y+y^2-58/5*x-58/5*y+203/5]

[676171/999999, x^2+x*y+y^2-14*x-14*y+55]

[61471/90909, x^2+6/5*x*y+y^2-76/5*x-76/5*y+311/5]

[225397/333333, x^2+7/5*x*y+y^2-82/5*x-82/5*y+347/5]

[676202/999999, x^2-3/4*x*y+y^2-9/2*x-9/2*y+5]

[6092/9009, x^2-1/2*x*y+y^2-6*x-6*y+14]

[676232/999999, x^2+32+y^2-9*x-9*y]

[3578/5291, x^2+1/4*x*y+y^2-21/2*x-21/2*y+41]

[676252/999999, x^2+1/2*x*y+y^2-12*x-12*y+50]

[225424/333333, x^2+x*y+y^2-15*x-15*y+68]

[676282/999999, x^2+5/4*x*y+y^2-33/2*x-33/2*y+77]

[676292/999999, x^2+3/2*x*y+y^2-18*x-18*y+86]

[676303/999999, x^2-4/3*x*y+y^2-2*x-2*y-3]

[61483/90909, x^2-x*y+y^2-4*x-4*y+9]

[677/1001, x^2-2/3*x*y+y^2-6*x-6*y+21]

[676334/999999, x^2-2/3*x*y+2/3*y^2-7*x-8/3*y+20]

[676343/999999, x^2+45+y^2-10*x-10*y]

[225451/333333, x^2+1/3*x*y+y^2-12*x-12*y+57]

[676373/999999, x^2+x*y+y^2-16*x-16*y+81]

[225461/333333, x^2+4/3*x*y+y^2-18*x-18*y+93]

[676393/999999, x^2+5/3*x*y+y^2-20*x-20*y+105]

[676414/999999, x^2-2*x*y+y^2+x+y-14]

[96632/142857, x^2-3/2*x*y+y^2-2*x-2*y+4]

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[54/77, x^2-74/109*x*y-59/109*y^2-648/109*x+864/109*y-805/109]

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[21310/30303, x^2+8/3*x*y+y^2-10*x-10*y+21]

[64/91, x^2+134/9*x*y+47/3*y^2-76*x-208*y+483]

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[6340/9009, x^2+8/7*x*y+4/3*y^2-11*x-40/3*y+28]

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[61/63, x^2+36/19*x*y+41/19*y^2-407/19*x-649/19*y+2598/19]

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[692/693, x^2-1/2*x*y+1/3*y^2-21/2*x-7/6*y+75/2]

[998656/999999, x^2-2/3*x*y+2/3*y^2-9*x-16/3*y+48]

[2999/3003, x^2-2/3*x*y+1/2*y^2-10*x-5/2*y+45]

[818/819, x^2-x*y+y^2-8*x-8*y+63]

>