Plot Labels with arrows or lines pointing to different curves?

[handwerk (Derek Handwerk)]

I’m trying to get plot labels with arrows or lines pointing to different curves. If I do

A2 = 1;
Plot[Evaluate@
  Table[Labeled[Sqrt[x^2 - x^4]/Sqrt[
    1 + A2 \[Beta]], \[Beta]], {\[Beta], {.1, .5, 1, 5, 10, 20}}], {x,
   0, 1.2}, AxesLabel -> {Subscript[k, x], Subscript[k, y]}, 
 PlotRange -> All, LabelStyle -> Directive[14, Bold]]

I get the following image.

How do I make the lines point to a better part of the curves?

I’ve also tried something along the lines of

Plot[Evaluate@
  Table[Sqrt[x^2 - x^4]/Sqrt[
   1 + \[Beta]], {\[Beta], {.1, .5, 1, 5, 10, 20}}], {x, 0, 1.2}, 
 PlotLabels -> 
  Placed[{"\[Beta] = .1", "\[Beta] = .5", "\[Beta] = 1", 
    "\[Beta] = 5", "\[Beta] = 10", "\[Beta] = 20"}, Above], 
 PlotRange -> All]

I’ve tried using Scaled[] as well. Those options seem to move the labels around but remove the lines pointing to the curves.

[timmy2x (Tim Laska)]

You may want to try experimenting with Callout[].

A2 = 1;
Manipulate[
 Plot[Evaluate@
   Table[Callout[Sqrt[x^2 - x^4]/Sqrt[1 + A2 \[Beta]], \[Beta], pos, 
     CalloutMarker -> "CirclePoint"], {\[Beta], {.1, .5, 1, 5, 10, 
      20}}], {x, 0, 1.2}, 
  AxesLabel -> {Subscript[k, x], Subscript[k, y]}, PlotRange -> All, 
  LabelStyle -> Directive[14, Bold], 
  ImageSize -> Large], {{pos, 0.8, "Position"}, 0, 1, 
  Appearance -> "Labeled"}]

Update

The LeaderSize option will give you more control over the callout placement. You can experiment with the manipulate below. For me, the largest effects were adjusting the Neck parameters.

A2 = 1;
m = Manipulate[
  Plot[Evaluate@
    Table[Callout[Sqrt[x^2 - x^4]/Sqrt[1 + A2 \[Beta]], \[Beta], pos, 
      Background -> White, 
      LeaderSize -> {{leadlen, horizangle Degree, gap}, {neck, 
         neckangle Degree}}, 
      CalloutMarker -> "CirclePoint"], {\[Beta], {.1, .5, 1, 5, 10, 
       20}}], {x, 0, 1.2}, 
   AxesLabel -> {Subscript[k, x], Subscript[k, y]}, PlotRange -> All, 
   LabelStyle -> Directive[14, Bold], 
   ImageSize -> Large], {{pos, 1/Sqrt[2], "Position"}, 0, 1, 
   Appearance -> "Labeled"}, {{leadlen, 40, "Leader Length"}, 0, 100, 
   Appearance -> "Labeled"}, {{horizangle, 225, 
    "Horizontal Angle(\[Degree])"}, -360, 360, 
   Appearance -> "Labeled"}, {{gap, 2, "Gap"}, 0, 10, 
   Appearance -> "Labeled"}, {{neck, 20, "Neck Length"}, 0, 100, 
   Appearance -> "Labeled"}, {{neckangle, 20, 
    "NeckAngle(\[Degree])"}, -360, 360, Appearance -> "Labeled"}]