$ \bf{R^2} $

$ \bf R $

$f(r)=(1-\lambda)r^2+\lambda Rr$

$r$

$\frac{A}{2\pi}$

A $\lambda=\frac{M}{R}$ paraméter 
változtatásával változik a kúp
alakja és a szélsőérték helye is.

λ = 3 (slider from 0 to 5, step 0.1)
R_1 = 2
a = CurveCartesian(t, (1 - λ) * t^(2) + λ * R_1 * t, t, -2 * R_1, 0)
A = Point(a)
R = Point(xAxis)
r_{minvec}: (If[λ > 1, Min[x(R), λ * x(R) / (2 * (λ - 1))], x(R)], 0)
r_{max} = Translate(A, r_{minvec})
f(x) = (1 - λ) * x^(2) + λ * x(R) * x
A_1: (x(r_{max}), f(x(r_{max})))
C = Point(yAxis)
h = Line(A, C)
E = Point(h)
F = Point(h)
v = Vector(F, E)
j = OrthogonalLine(A_1, v)
p_1 = 3
P = Point({2, 4})
b = CurveCartesian(t, (1 - λ) * t^(2) + λ * R_1 * t, t, R_1, 3 * R_1)
g = CurveCartesian(t, (1 - λ) * t^(2) + λ * R_1 * t, t, 0, R_1)
c = Segment(A, R)
d = Segment(A, R)
B = Point(xAxis)
e = Ray(R, B)
D = Point(xAxis)
r = Point(e)
u = Vector(R, r)
i = OrthogonalLine(r_{max}, c)
k = OrthogonalLine(R, c)
J = Intersect(j, k)
I = Intersect(h, j)
l = Segment(I, J)
M: λ * x(R)
G = (-3.0909090909090904, 0.016363636363641118)
p = Circle(G, x(R))
m = OrthogonalLine(G, v)
K = Intersect(p, m, 1)
L = Intersect(p, m, 2)
n = OrthogonalLine(G, m)
q = Circle(G, M)
N = Intersect(q, n, 1)
O = Intersect(p, n, 2)
Q = Midpoint(L, G)
S = Midpoint(G, K)
s = OrthogonalLine(Q, m)
t = OrthogonalLine(S, m)
T = Intersect(p, s, 2)
U = Intersect(p, t, 2)
T' = Dilate(T, 0.3, Q)
O' = Dilate(O, 0.3, G)
U' = Dilate(U, 0.3, S)
c_1 = Conic(L, T', O', U', K)
a_1 = Segment(N, L)
b_1 = Segment(N, K)
d_1 = Circle(G, x(r_{max}))
V = Intersect(d_1, m, 1)
W = Intersect(d_1, m, 2)
μ: Distance[G, V] / Distance[G, K]
e_1 = Dilate(c_1, μ, G)
f_1 = OrthogonalLine(W, m)
Z = Intersect(f_1, a_1)
w = Vector(W, Z)
g_1 = Translate(e_1, Vector[(0.018181818181818077, 0)])
h_1 = Translate(g_1, w)
V' = Translate(V, w)
i_1 = Segment(V', V)
j_1 = Segment(Z, W)