How to make this model in wolfram mathematica?

A model production possibility curve (nonlinear case).
I used 1/4 of a circle in the code.

Manipulate[ 
ParametricPlot[{{12 Cos[t],6 Sin[t]}}, {t, 
 0, Pi/2},GridLines->Automatic, PlotRange->{{0,15},{0,10}},
AxesOrigin -> {0, 0} ,
LabelStyle -> Directive[12], 
PlotLabel->"Кривая Производственных Возможностей",
AxesLabel->{"товар Х","товар У"},
Epilog -> {PointSize[.05], Point[{{12 Cos[t],6 Sin[t]}}]}], {t, 
 0, Pi/2}]

I can not make a calculation of points on the curve when driving using the dotted line.
Mail can throw off the image of what should be a model.
thanks for the help.

Manipulate[ParametricPlot[{{12 Cos[t], 6 Sin[t]}}, {t, 0, Pi/2}, 
  GridLines -> Automatic, PlotRange -> {{0, 15}, {0, 10}}, 
  AxesOrigin -> {0, 0}, LabelStyle -> Directive[12], 
  PlotLabel -> "Кривая Производственных Возможностейn 
    точка =" <> ToString[{12 Cos[t], 6 Sin[t]}], 
  AxesLabel -> {"товар Х", "товар У"}, 
  Epilog -> {PointSize[.05], Point[{{12 Cos[t], 6 Sin[t]}}], Red, 
    Dotted, Line[{{0, 6 Sin[t]}, {15, 6 Sin[t]}}], 
    Line[{{12 Cos[t], 0}, {12 Cos[t], 10}}]}], {{t, .5}, 0, Pi/2}]