\text{Zostrojte obraz kružnice }k(O,r=OM) \text{ v stredovej kolineácii }\mathscr{K}(S,o,u).

1

1. \; \text{Zvoľme ľub. body: }L∈k,1∈o

2. \; \text{Úbežník }U=\overleftrightarrow{1L}∩u

3.  \; \text{Bod }(1=1')∈\mathscr{K}(\overleftrightarrow{1L}) \; ∧ \; \mathscr{K}(\overleftrightarrow{1L}) ∥\overleftrightarrow{SU}=\overrightarrow{v}

4. \; \text{Odkiaľ: }\mathscr{K}(L)=L'∈\overleftrightarrow{SL}

5. \; \text{Kužeľosečka ako množina bodov: }\left\{ L'→L \right\} 

S = (-0.86114, 11.468338181818194)
A = (-3, 1)
B = (11, 1)
o = Line(A, B)
C = (3.2297690909091017, 8.941065454545464)
u = Line(C, o)
O = (2.2276963636363742, 2.86092)
M = (-3.2520309090909043, 2.458556363636375)
k = Circle(O, M)
L = Point(k)
D = Point(o)
g = Line(L, D)
U = Intersect(u, g)
h = Line(S, U)
i = Line(D, h)
v = Vector(S, U)
f = Line(S, L)
L' = Intersect(f, i)
GMB1 = Locus(L', L)