P_2 = (1, -2)
y_2: y(P_2)
x_2: x(P_2)
P_1 = (4, 3)
y_1: y(P_1)
x_1: x(P_1)
d: (y_1^(2) * x_2) - (y_2^(2) * x_1)
c: (y_1 * (y_2 * (y_1 - y_2))) + ((2 * x_1) * (x_2 * (y_2 - y_1)))
b: (x_1 * (x_2 * (x_1 - x_2))) + (((2 * (x_2 - x_1)) * y_1) * y_2)
a: (x_1^(2) * y_2) - (x_2^(2) * y_1)
f = Simplify(((a * x^(3)) + (b * x^(2)) + (c * x) + d) / a)
A, B, C = Intersect(f, xAxis)
O = Point(xAxis)
axe: y = (x(A) * x)
ts = OrthogonalLine(O, axe)
ph_2 = OrthogonalLine(P_2, ts)
H_2 = Intersect(ts, ph_2)
T_2 = Midpoint(O, H_2)
t_2 = Line(P_2, T_2)
pf_2 = Mirror(ph_2, t_2)
F = Intersect(axe, pf_2)
F' = Mirror(F, ts)
dir = OrthogonalLine(F', axe)
e = Parabola(F, dir)
ph_1 = OrthogonalLine(P_1, ts)
H_1 = Intersect(ts, ph_1)
T_1 = Midpoint(H_1, O)
t_1 = Line(P_1, T_1)
pf_1 = Mirror(ph_1, t_1)
xb: x(B)
xc: x(C)
xa: x(A)
texte6: "f(x) = " + (LaTeX[f]) + "\\
\\
x_a =" + (LaTeX[xa]) + ", \, x_b =" + (LaTeX[xb]) + ", \, x_c =" + (LaTeX[xc]) + "\\
axe : " + (LaTeX[axe]) + ""