A = (12.474546433821686, 7.201959804231775)
B: (0, 0)
c = Segment(A, B)
C: (197 / 13, 0)
b = Segment(C, A)
a = Segment(B, C)
cubicEqn = TriangleCurve(A, B, C, 0 = ((((a^(2) * B^(3)) * (a - c)) * c^(2)) * (a + c)) - ((((A^(3) * b^(2)) * (b - c)) * c^(2)) * (b + c)) + (((((A^(2) * B) * (b - c)) * c^(2)) * (b + c)) * ((2 * a^(2)) - (3 * b^(2)) - (2 * c^(2)))) + (((((A * B^(2)) * (a - c)) * c^(2)) * (a + c)) * ((3 * a^(2)) - (2 * b^(2)) + (2 * c^(2)))) + (((((((((4 * A) * (a - b)) * (a + b)) * B) * (a - c)) * (b - c)) * (a + c)) * (b + c)) * C) + (((((A^(2) * b^(2)) * (b - c)) * (b + c)) * ((2 * a^(2)) - (2 * b^(2)) - (3 * c^(2)))) * C) + (((((a^(2) * B^(2)) * (a - c)) * (a + c)) * ((2 * a^(2)) - (2 * b^(2)) + (3 * c^(2)))) * C) - (((((A * (a - b)) * b^(2)) * (a + b)) * ((3 * a^(2)) + (2 * b^(2)) - (2 * c^(2)))) * C^(2)) - (((((a^(2) * (a - b)) * (a + b)) * B) * ((2 * a^(2)) + (3 * b^(2)) - (2 * c^(2)))) * C^(2)) - ((((a^(2) * (a - b)) * b^(2)) * (a + b)) * C^(3)))
MoveMe = Point(cubicEqn)
AB = Line(A, B)
BC = Line(B, C)
CA = Line(C, A)
barysP = Element(Transpose[ReducedRowEchelonForm[{{x(A), x(B), x(C), x(MoveMe)}, {y(A), y(B), y(C), y(MoveMe)}, {1, 1, 1, 1}}]], 4)
CIP = Barycenter({A, B, C}, {((((barysP(1) * (barysP(1) + barysP(2) + barysP(3))) * a^(2)) * b^(2)) * c^(2)) + ((a^(2) * ((-a^(2)) + b^(2) + c^(2))) * (((barysP(2) * barysP(3)) * a^(2)) + ((barysP(1) * barysP(3)) * b^(2)) + ((barysP(1) * barysP(2)) * c^(2)))), ((((barysP(2) * (barysP(1) + barysP(2) + barysP(3))) * a^(2)) * b^(2)) * c^(2)) + ((b^(2) * (a^(2) - b^(2) + c^(2))) * (((barysP(2) * barysP(3)) * a^(2)) + ((barysP(1) * barysP(3)) * b^(2)) + ((barysP(1) * barysP(2)) * c^(2)))), ((((barysP(3) * (barysP(1) + barysP(2) + barysP(3))) * a^(2)) * b^(2)) * c^(2)) + ((c^(2) * (a^(2) + b^(2) - c^(2))) * (((barysP(2) * barysP(3)) * a^(2)) + ((barysP(1) * barysP(3)) * b^(2)) + ((barysP(1) * barysP(2)) * c^(2))))})
x3 = TriangleCenter(A, B, C, 3)
x1 = TriangleCenter(A, B, C, 1)
x6 = TriangleCenter(A, B, C, 6)
x155 = TriangleCenter(A, B, C, 155)
x399 = TriangleCenter(A, B, C, 399)
FOfT = Conic(x1, x3, x6, x155, x399)