Angle bisector formed by a parabola

						JXG.Options.text.useKatex = true;
JXG.Options.axis.ticks.majorHeight = 10;
JXG.Options.axis.ticks.insertTicks = false;
JXG.Options.axis.ticks.ticksDistance = 100;
var board = JXG.JSXGraph.initBoard('box1', {
boundingbox:[-6, 6, 6, -2],showNavigation:false, showcopyright: false, axis: true,
});

 
var h =0;
var p = 1;
var k = 0
 
var f1 = board.create('functiongraph',[function(x){ return (x-h)*(x-h)/4/p+ k;}, -100, 100],{strokeColor:'red'});
 var p1 = board.create('point', [h,k+p],{name:'M',size:0,fixed:true,label:{offset:[-25,15]}});
 var pn = board.create('point', [h,-k-p],{name:'N',size:0,fixed:true,label:{offset:[10,-15]}});
  
var p2 = board.create('point', [h,k],{name:'O',size:0,fixed:true,label:{offset:[5,15]}});
var f2 = board.create('functiongraph',[k-p, -12, 25],{strokeColor:'red'});

 var g1 = board.create('glider', [3, 3, f1],{name:'P'});
 var l1 = board.create('segment', [p1, g1]);
 var i1 = board.create('intersection', [l1, f1 ],{name:'Q',size:0,label:{offset:[-25,10]}});
 var l3 = board.create('segment', [p1, i1]);
  var g2 = board.create('glider', [-4.0, 8, f2],{visible:false});
  var g3 = board.create('glider', [-1.0, 8, f2],{visible:false});
  var l2 = board.create('segment', [g2, g3],{withLabel:true, name:'l',color:'transparent', label:{offset:[-10,-10]},});
 var pp1 = board.create('perpendicularpoint', [g1, l2],{name:'H',size:0});
  var fe = board.create('perpendicularsegment', [l2, g1],{dash:2});
  var pp1 = board.create('perpendicularpoint', [i1, l2],{name:'R',size:0,label:{offset:[-25,10]}});
  var fe2 = board.create('segment', [i1, pp1],{dash:2});
  var l4 = board.create('segment', [i1, pn]);
  var l5 = board.create('segment', [g1, pn]);