Author: franco ghione
Date: 7 Novembre 2015

$ a $

$ c $

Zoom +

Zoom -

$ x^3+p^3=ax^2 $

$ p=\sqrt[3]{c} $

$ xy=p^2 $

$ y^2=p(a-x) $

$ \frac{p^2}{x^2}=\frac{y}{p}×\frac{a-x}{y} $

$ x_1 $

$ x_2 $

$ x_3 $

Axis +

Axis -

(p,p)

\frac{p}{x}=\frac{y}{p}=\frac{a-x}{y}

MUOVI \  \  \  a 
\   \     E \ \ \  c

a = 6 (slider from 0 to 50, step 1)
c = 9 (slider from 1 to 150, step 1)
O = (0, 0)
P: O + (1, 0)
d = Line(O, P)
e = OrthogonalLine(O, d)
p: c^(1 / 3)
f(x) = (p * p / x)
g(x) = ((p * (a - x)))^(1 / 2)
testo2: "$ x^3+" + (LaTeX[c]) + "=" + (LaTeX[a]) + "x^2 $"
A, B = Intersect(f, g, 0, 100)
b = OrthogonalLine(A, d)
h = OrthogonalLine(B, d)
C = Intersect(d, b)
D = Intersect(d, h)
i = Segment(A, C)
j = Segment(B, D)
r(x) = (-((p * (a - x)))^(1 / 2))
F = Intersect(r, f, -10, 0)
k = OrthogonalLine(F, d)
G = Intersect(d, k)
l = Segment(G, F)
T: (p, p)
m = OrthogonalLine(T, e)
n = OrthogonalLine(T, d)
E = Intersect(e, m)
H = Intersect(d, n)
poligono1, e_1, t, h_1, o = Polygon(E, T, H, O)
x_1: x(B)
x_2: x(A)
x_3: x(F)
R: (a, 0)
q = Segment(O, R)
testo13: "a=" + a + ""
s = Segment(E, O)
testo14: "p=" + p + ""
testo15: "$ x_1=" + (LaTeX[x_1]) + " $"
testo16: "$ x_2=" + (LaTeX[x_2]) + " $"
testo17: "$ x_3=" + (LaTeX[x_3]) + " $"