read Conic:
read pyth_LLL:  # uncomment one line in that file if you have Maple 9


a,b,c := 1, 32*u^2+16*v*u-4*v^2, -8*v*u^3+8*u*v^3-12*v^4+8*u^2*v^2-12*u^4 ;
pt := Conic(a,b,c);
check := expand(a*pt[1]^2 + b*pt[2]^2 + c*pt[3]^2);


a,b,c := 1, 3, -x^4+2*x^3-5*x^2+4*x-19;
pt := Conic(a,b,c);
check := expand(a*pt[1]^2 + b*pt[2]^2 + c*pt[3]^2);


a,b,c := 3*t2^2-12*t2+15, 757*t2^2-108*t2^3+1-27*t2^4-868*t2, 216*t2+27*t2^2-4;
pt := Conic(a,b,c);
check := expand(a*pt[1]^2 + b*pt[2]^2 + c*pt[3]^2);


a,b,c := -49*t1^3-56*t1^4+392*t1-196, -287*t1^2-4900*t1+2401,
        7*t1^4+2761*t1^2-11*t1^3+564+5193*t1;
pt := Conic(a,b,c);
check := expand(a*pt[1]^2 + b*pt[2]^2 + c*pt[3]^2);


a,b,c := -27536*t^4+264718-590981*t+318906*t^2-491948*t^3,
       548716*t^3-73434+70688*t-420780*t^2-405542*t^4+119857*t^5,
       73434+223048*t+460782*t^2+394745*t^3+193364*t^4-119857*t^5;
pt := Conic(a,b,c);
check := expand(a*pt[1]^2 + b*pt[2]^2 + c*pt[3]^2);


a,b,c := (246793*t^4+146591+127983*t-392396*t^2-164181*t^3)*
       (48688*t^3-21163+91633*t-22739*t^2-145764*t^4+69378*t^5)*(t-1)*
       (69378*t^6+201126*t^5+291160*t^4-309559* t^3+68894*t^2+70470*t-21163),
       -246793*t^6-169330*t^2-79295*t^3+246632*t^4+233559*t^5-21163+91633*t,
        167754-299158*t+354087*t^2-323593*t^3+115045*t^4-69378*t^5;
pt := Conic(a,b,c);
check := expand(a*pt[1]^2 + b*pt[2]^2 + c*pt[3]^2);


a,b,c := 4-3*t+4*t^2, 24-20*t+12*t^2-24*t^4, -28+71*t-64*t^2+24*t^4;
pt := Conic(a,b,c);
check := expand(a*pt[1]^2 + b*pt[2]^2 + c*pt[3]^2);


a,b,c := 1, 1+4*t-t^2, -2-2*s-s^2-4*t+2*s*t-13*t^2-2*s*t^2+2*s*t^3-8*t^3-9*t^4;
pt := Conic(a,b,c);
check := expand(a*pt[1]^2 + b*pt[2]^2 + c*pt[3]^2);


a,b,c := -2*s-2-s^2,
       1-8*s*t-8*t-4*t*s^2+2*s*t^2+2*t^2+t^2*s^2,
       1+26*t*s^2+18*s*t+16*t*s^3+4*t*s^4+2*t+20*t^2*s^2+30*s*t^2
       +4*t^2*s^3-t^2*s^4+17*t^2+10*t^3+24*t^3*s+6*t^3*s^3+18*t^3*s^2
       +15*t^4+4*t^4*s^2-2*t^4*s^3+12*t^4*s;
pt := Conic(a,b,c);
check := expand(a*pt[1]^2 + b*pt[2]^2 + c*pt[3]^2);