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Familia de hipérbolas al variar k

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Determina los valores de  a, b y k 
de la hipérbola que se muestra.

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¡ Muy bien !

y=a+\frac{k}{x-b}

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¡ Muy bien !

Has completado 
correctamente
el ejercicio.

b2 = 1 (slider from -4 to 4, step 1)
t(x) = x - b2
a2 = 3 (slider from -4 to 4, step 1)
k2 = -2 (slider from -6 to 6, step 1)
k = 2 (slider from -12 to 12, step 1)
a = 0 (slider from -6 to 6, step 1)
b = 0 (slider from -6 to 6, step 1)
f(x) = a + k / (x - b)
c: y = a
d: x = b
e = false
zoom: 0
A = Point(f)
g = Line(A, xAxis)
h = Line(A, yAxis)
B = Intersect(d, g)
C = Intersect(c, h)
D = Intersect(c, d)
polígono1, d_1, b_1, a_1, c_1 = Polygon(D, B, A, C)
i: false
j = false
a1 = Random(-4, 4)
ejer: 0
k11 = Random(-6, 5)
k1 = If(k11 ≟ 0, 6, k11)
b1 = Random(-4, 4)
f1(x) = a1 + k1 / (x - b1)
l: false
m: y = a1
n: x = b1
est1 = 0 (slider from 0 to 2, step 1)
ac1: k1 ≟ k2 ∧ a1 ≟ a2 ∧ b1 ≟ b2
texto5: "y=" + (LaTeX[a2]) + "+\frac{" + (LaTeX[k2]) + "}{" + (LaTeX[t]) + "}"
p(x) = a2 + k2 / (x - b2)
texto8: "" + (LaTeX[texto5]) + ""
aciertos1: 0
E = (-4, -2.5)
lista2 = Sequence(Circle[E + (i * (0.5, 0)), 0.2], i, 1, aciertos1)
texto12: "y=" + (LaTeX[a]) + ""
lista1 = Sequence(a + i / (x - b), i, -36, 36)
texto14: "x=" + (LaTeX[b]) + ""
q = Segment(D, C)
texto16: "" + c_1 + ""
r = Segment(D, B)
texto17: "" + d_1 + ""
o: abs(k)
texto13: "y=" + (LaTeX[a]) + " \; "
texto15: "Área rectángulo = " + o + ""
s(x) = x - b
texto18: "y=" + (LaTeX[a]) + "+\frac{k}{" + (LaTeX[s]) + "}"
texto3: "a=" + (LaTeX[a2]) + ""
texto4: "b=" + (LaTeX[b2]) + ""
texto2: "k=" + (LaTeX[k2]) + ""
F = Point(f1)
e_1 = OrthogonalLine(F, m)
f_1 = OrthogonalLine(F, n)
G = Intersect(m, e_1)
H = Intersect(n, f_1)
I = Intersect(m, n)
polígono2, i_1, g_1, f_2, h_1 = Polygon(I, G, F, H)
j_1 = Segment(I, G)
k_1 = Segment(I, H)
texto19: "" + i_1 + ""
texto20: "" + h_1 + ""
s1(x) = x - b1
texto21: "y=" + (LaTeX[a1]) + "+\frac{" + (LaTeX[k1]) + "}{" + (LaTeX[s1]) + "}"
texto23: "y=\frac{k}{" + (LaTeX[s]) + "}"
texto10: "y=" + (LaTeX[a]) + "+\frac{" + (LaTeX[k]) + "}{" + (LaTeX[s]) + "}"
texto24: "y=\frac{" + (LaTeX[k]) + "}{" + (LaTeX[s]) + "}"