$\textsf{\LARGE A}$

T-Circle

T-Ellipse

T-Parabola

$\textsf{\LARGE r}$

T-Hyperbola

The T-ellipse generally has the shape of an octagon. If points A and B 
lie on the same vertical or horizontal line, it takes on a hexagonal shape.
When the constant coincides with the T-distance from A to B, the ellipse 
degenerates into a rectangle with diagonal AB.

$\textsf{\LARGE B}$

The T-parabola is generally formed by 
two rays (either horizontal or vertical) 
and two segments.

As we have seen before, the T-circle takes on
a square shape (with diagonals parallel to the axes).

Each branch of the T-hyperbola is generally formed by 
two rays (either horizontal or vertical) and one segment.

Activate offset

XB − Xr =0

A: (-4.35275, 1.08819)
I: (-3.75, 0.75)
s = Line(A, I)
op1 = true
rr = 4 (slider from 0 to 8, step 0.02)
op2 = false
op3 = false
r = OrthogonalLine(A, s)
op4 = false
B = Point(s)
dAB: abs(x(B)) + abs(y(B))
B_1: (1, -0.25)
ver2 = false
ver3 = false
ver4 = false
m: ((-x(r))) / y(r)
kh: 3
C: (1.25, -0.25)
ke: 10
a = PathParameter(B)
l1: {Polygon[A - (0, rr), A + (rr, 0), 4]}
b = PathParameter(A)
c: 0.83249
Xr(x, y) = abs((x(r) * x) + (y(r) * y) + z(r)) / Max[abs(x(r)), abs(y(r))]
XB(x, y) = abs(x - x(B)) + abs(y - y(B))
XA(x, y) = abs(x - x(A)) + abs(y - y(A))
ec2:=XA + XB = ke
op5 = false
rr': 8 - rr
sB: {Polygon[B - (rr', 0), B - (0, rr'), 4]}
sAe: {Polygon[A - (ke - rr', 0), A - (0, ke - rr'), 4]}
sAh: {Polygon[A - (kh + rr', 0), A - (0, kh + rr'), 4]}
r1 = Translate(r, If[y(r) ≤ (-x(r)) ∨ y(r) ≟ 0, (rr', 0), (0, (-rr'))])
r2 = Translate(r, If[y(r) ≤ (-x(r)) ∨ y(r) ≟ 0, ((-rr'), 0), (0, rr')])
ec3:=XB - Xr = 0
ec1:=XA - rr = 0
ec4:=XA - XB = kh
texto5: "XA + XB = " + ke + ""
texto6: "XA − XB = " + kh + ""
texto7: "XA − " + rr + " = 0"

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)