r_1

r_2

r_3

r_4

P'

P''

P'''

P

P''''

escala = 50 (slider from 1 to 100, step 1)
B = Point(yAxis)
b: y(B)
b2: floor(b + 0.01)
T1: "" + (floor(b + 1.0E-4))
A = Point(yAxis)
a: y(A)
a2: floor(a + 0.01)
T2: "" + (floor(a + 1.0E-4))
h(x) = (x^(4) - 2 * (a2 + b2) * x^(2) + (a2 - b2)^(2)) / escala
R1: (-sqrt(a2) - sqrt(b2), 0)
R2: (-sqrt(a2) + sqrt(b2), 0)
R3: (sqrt(a2) - sqrt(b2), 0)
R4: (sqrt(a2) + sqrt(b2), 0)
f1(x) = h'(x)
P1: (x(R1), f1(x(R1)))
signoP1: sgn(y(P1))
P2: (x(R2), f1(x(R2)))
signoP2: sgn(y(P2))
P3: (x(R3), f1(x(R3)))
signoP3: sgn(y(P3))
P4: (x(R4), h'(x(R4)))
signoP4: sgn(y(P4))
f2(x) = h''(x)
S1: (x(R1), f2(x(R1)))
signoS1: sgn(y(S1))
S2: (x(R2), f2(x(R2)))
signoS2: sgn(y(S2))
S3: (x(R3), f2(x(R3)))
signoS3: sgn(y(S3))
S4: (x(R4), f2(x(R4)))
signoS4: sgn(y(S4))
f3(x) = f2'(x)
V1: (x(R1), f3(x(R1)))
signoV1: sgn(y(V1))
V2: (x(R2), f3(x(R2)))
signoV2: sgn(y(V2))
V3: (x(R3), f3(x(R3)))
signoV3: sgn(y(V3))
V4: (x(R4), f3(x(R4)))
signoV4: sgn(y(V4))
f(x) = x^(2) + b
R_1 = If(y(B) ≟ 0, Intersect[f, xAxis, 1], Intersect[f, xAxis, 2])
g(x) = x^(2) + a
R_2 = If(y(A) ≟ 0, Intersect[g, xAxis, 1], Intersect[g, xAxis, 2])
O = (0, 0)
c = Circle(O, R_1)
Q1: (0, x(R_1))
e = CircleArc(O, R_1, Q1)
r = OrthogonalLine(Q1, yAxis)
s = OrthogonalLine(R_2, xAxis)
Q2 = Intersect(r, s)
k = Circle(R_2, Q2)
p = CircleArc(R_2, R4, Q2)
F = (8, 6)
G = (8, 5)
H = (8, 4)
I = (8, 3)
ver1 = false
ver2 = false
ver3 = false
s11 = Segment(R1, P1)
s12 = Segment(P2, R2)
s13 = Segment(R3, P3)
s14 = Segment(P4, R4)
s21 = Segment(S1, R1)
s22 = Segment(R2, S2)
s23 = Segment(R3, S3)
s24 = Segment(S4, R4)
s31 = Segment(R1, V1)
s32 = Segment(R2, V2)
s33 = Segment(V3, R3)
s34 = Segment(V4, R4)
ver = true
f4(x) = f3'(x)
W1: (x(R1), f4(x(R1)))
W2: (x(R2), f4(x(R2)))
W3: (x(R3), f4(x(R3)))
W4: (x(R4), f4(x(R4)))
s41 = Segment(W1, R1)
s42 = Segment(W2, R2)
s43 = Segment(W3, R3)
s44 = Segment(W4, R4)
ver4 = false
T5: "raíces = \pm\left(\sqrt{" + (LaTeX[b2]) + "}\pm \sqrt{" + (LaTeX[a2]) + "}\right)"
P = Simplify(h)
T4 = LaTeX(P, true, true)