How to put a point created by Epilog in a Legend?

Question

I want to put a point in the legend, which is the easiest way?

My code is:

Plot[x^2, {x, 0, 2}, 
 Epilog -> {Directive[Red, PointSize[Large]], Point[{1, 1}]}, 
 PlotLegends -> {"x^2"}]

This gives me the legend of the parabola but if I add another entry it does not print the point in the legend. What should I add?

Thanks so much in advance

Answer 1

plot1 = Plot[x^2, {x, 0, 2}, PlotLegends -> {"x^2"}];
plot2 = ListPlot[{{1, 1}}, PlotStyle -> Red, 
   PlotLegends -> {"A Red Dot"}];
Show[plot1, plot2]

Answer 2

Epilog puts graphics primitives after the plot is drawn. The legend has to be put together manually.

Plot[x^2, {x, 0, 2}
 , Frame -> True
 , ImageSize -> 400
 , Epilog -> {AbsolutePointSize[6], Red, Point@{1, 1}}, 
 PlotLegends -> Placed[LineLegend[{Blue, Blue}
    , {"\!\(\*SuperscriptBox[\(x\), \(2\)]\)", "Red dot"}
    , LegendLayout -> {"Column", 1}
    (*,LegendFunction\[Rule](Framed[#
    ,Background\[Rule]GrayLevel[0.9]
    ,RoundingRadius\[Rule]4]&)*)
    , LegendMarkers -> {"",
      Graphics[{Red, Disk[]}]}], {1, 0.5}]]