2
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Assume that G defined by:

G = {Sqrt[1 - x] + I Sqrt[x], Sqrt[1 - x] - I Sqrt[x]}

I am trying to create a point that moves along the curves of G from x=0.01 to x=0.99 using manipulate. I'm trying to adapt this code:

Manipulate[Show[ParametricPlot[Evaluate[ReIm /@ G], {x, 0.01, y}, AxesLabel -> (Style[#, 12, Bold] & /@ {Re, Im}),PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2}}, PlotLegends -> Placed[G, Right]], Graphics@{Dotted, Circle[{0, 0}, 1]}], Row[{Control[{{y, 0.011, "x"}, 0.011, 0.99,Slider[##, Appearance -> "Labeled"] &}], Control[{{y, 0.011, ""}, 0.011, 0.99, Animator[##, AnimationRunning -> False, AppearanceElements -> {"StepLeftButton", "StepRightButton", "PlayPauseButton", "DirectionButton"}] &}]}]]

This gives a rising curves between the values of x. I want to show the curves with a moving points of x-values along them. As the example here

Create a moving plot along a parametric plot using Manipulate?

but in 2D.

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I used Epilog inside of ParametricPlot to make the moving point.

Manipulate[Show[
  ParametricPlot[Evaluate[ReIm /@ G], {x, 0.01, y}, 
   AxesLabel -> (Style[#, 12, Bold] & /@ {Re, Im}),
   PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2}},
   PlotLegends -> Placed[G, Right],
   Epilog -> {PointSize[Large], Point[Evaluate[ReIm /@ (G /. x -> y)]]}
   ]
  ,
  Graphics@{Dotted, Circle[{0, 0}, 1]}
  ], 
  {y, 0, 1}
 ]

enter image description here

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2
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Manipulate[
 ParametricPlot[Evaluate[ReIm /@ G], {x, 0.01, y}, 
  AxesLabel -> (Style[#, 12, Bold] & /@ {Re, Im}), 
  PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2}}, MeshFunctions -> {#3 &}, 
  Mesh -> {{y}}, MeshStyle -> Directive[Red, PointSize[Large]], 
  Epilog -> {Dotted, Circle[{0, 0}, 1]}, 
  PlotLegends -> Placed[G, Right]], 
 Row[{Control[{{y, 0.011, "x"}, 0.011, 0.99, 
     Slider[##, Appearance -> "Labeled"] &}], 
   Control[{{y, 0.011, ""}, 0.011, .99, 
     Animator[##, AnimationRunning -> False, 
       AppearanceElements -> {"StepLeftButton", "StepRightButton", 
         "PlayPauseButton", "DirectionButton"}] &}]}]]

enter image description here

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