# Create a moving point along a parametric plot using Manipulate?

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.

• Replace the Graphics part with Graphics[{{Dotted, Circle[{0, 0}, 1]}, {Red, Point /@ Evaluate[ReIm /@ G /. x -> y]}}] – MeMyselfI Feb 1 '19 at 21:34
• Similar to @kglr's solution: mathematica.stackexchange.com/questions/190189/… – Michael E2 Feb 2 '19 at 0:05

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}
] 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"}] &}]}]] 