k > 1

Checking

$\textsf{\LARGE A}$

   POINT- LINE
Constant quotient

When the quotient of the distances of the points of the searched locus
to point A and the line r is a constant less than 1, we obtain a ellipse.
(That constant is the eccentricity.)

$\textsf{\LARGE r}$

0 < k < 1

k = 1

When the quotient of the distances of the points of the searched locus
to point A and the line r is a constant equal to 1, we obtain a parabola.
(That constant is the eccentricity.)

When the quotient of the distances of the points of the searched locus
to point A and the line r is a constant greater than 1, we obtain a hyperbola.
(That constant is the eccentricity.)

Activate offset

XA / Xr = k

op3 = false
C: (1.4, 3.8)
h = 6 (slider from 0 to 6, step 0.02)
k = 0.6 (slider from 0 to 3, step 0.1)
comprobar = false
A: (3, 0)
s1 = Segment(C, A)
r = Line((0, -0.04), (3, 3.96))
B: (3.25, -1)
op1 = true
op2 = false
Pd = ClosestPoint(r, C)
s2 = Segment(C, Pd)
kk: Distance[C, A] / Distance[C, Pd]
textoComprueba: "k = " + kk + ""
ci:=XA / Xr = k
op4 = false
h': 6 - h
r1 = Translate(r, Vector[(h' * UnitOrthogonalVector[r])])
r2 = Translate(r, Vector[((-h') * UnitOrthogonalVector[r])])
sA = Circle(A, (k * h'))

Tool: OpSuma
Elige O y luego dos puntos
Input: O, A, B
Output: O'

C = Midpoint(A, B)
O' = Mirror(O, C)

Tool: OpResta
Elige O, el primer punto y el segundo punto
Input: O, A, B
Output: O'

B' = Mirror(B, O)
C = Midpoint(A, B')
O' = Mirror(O, C)

Tool: OpProducto
Elige O e I, y luego dos puntos
Input: O, I, A, B
Output: E

I' = Mirror(I, O)
B' = Mirror(B, O)
c = Semicircle(I', I)
d = Semicircle(B', B)
f = Line(O, I)
g = OrthogonalLine(O, f)
C = Intersect(c, g, 1)
h = Line(C, A)
D = Intersect(d, g, 1)
i = Line(D, h)
E = Intersect(f, i)

Tool: OpDivisión
Elige O e I, y luego el primer punto y el segundo punto
Input: O, I, A, B
Output: E

f = Line(O, I)
g = OrthogonalLine(O, f)
I' = Mirror(I, O)
c = Semicircle(I', I)
Binv = Mirror(B, c)
Binv' = Mirror(Binv, O)
e = Semicircle(Binv', Binv)
F = Intersect(e, g, 1)
C = Intersect(c, g, 1)
h = Line(C, A)
i = Line(F, h)
E = Intersect(f, i)