Manipulate[randomX=(randomY^2)/2;curve=ContourPlot[y^2==2*x,{x,-1,20},{y,-5,5},PlotTheme->"Detailed", PlotPoints->100,ImageSize->400];randomPoint=Graphics[{Blue,PointSize[0.02],Point[{randomX,randomY}]}];line=Graphics[{Orange,Thickness[0.01],Line[{{randomX,randomY},{1,4}}]}];lineLength=EuclideanDistance[{randomX,randomY},{1,4}];Column[{Show[curve,randomPoint,line,Epilog->Text[ToString[{randomX,randomY}],{randomX+0.5,randomY}]],Row[{"Line Length:", lineLength}]},Alignment->Top],{{randomY,0,"RandomY"}, -5,5,Appearance->"Labeled"}]
Out[]=
