Hide / Unhide parabolas

a = 2 (slider from -10 to 10, step 0.1)
b = 5 (slider from -10 to 10, step 0.1)
c = 6 (slider from -10 to 10, step 0.1)
d = 6 (slider from -10 to 10, step 0.1)
eastVector = Vector((1, 0))
westVector = Vector((-1, 0))
northVector = Vector((0, 1))
southVector = Vector((0, -1))
A_0 = (0, 0)
A_1 = Dilate(Translate[A_0, eastVector], a, A_0)
A_2 = Dilate(Translate[A_1, northVector], b, A_1)
A_3 = Dilate(Translate[A_2, westVector], c, A_2)
A_4 = Dilate(Translate[A_3, southVector], d, A_3)
lineA1A2 = Line(A_1, northVector)
lineA2A3 = Line(A_2, westVector)
lineA3A4 = Line(A_3, southVector)
B_1 = Point(lineA1A2)
B_2 = Intersect(lineA2A3, OrthogonalLine[B_1, Line[B_1, A_0]])
B_3 = Intersect(lineA3A4, OrthogonalLine[B_2, Line[B_2, B_1]])
lineA0A1 = Line(A_0, eastVector)
segmentA0A1 = Segment(A_0, A_1)
segmentA1A2 = Segment(A_1, A_2)
segmentA2A3 = Segment(A_2, A_3)
segmentA3A4 = Segment(A_3, A_4)
reflectedLineForA4 = Line(Mirror[A_4, lineA2A3], lineA2A3)
reflectedLineForA0 = Line(Mirror[A_0, lineA1A2], lineA1A2)
segmentA0B1 = Segment(A_0, B_1)
segmentB1B2 = Segment(B_1, B_2)
segmentB2B3 = Segment(B_2, B_3)
M = (-7.137308193634631, 8.638658362865463)
N = (20.735363081415336, -6.815496007459246)
resultedLine = Line(M, N)
A_4reflected = Mirror(A_4, resultedLine)
A_0reflected = Mirror(A_0, resultedLine)
parabolA0 = Parabola(A_0, reflectedLineForA0)
parabolA4 = Parabola(A_4, reflectedLineForA4)
coefs: {1, 2, 3}
e = false