Derivation of directrix equation for an ellipse

						
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:[-10, 10, 10, -10],showNavigation:false, showcopyright: false, axis: true,
});

 var F1 = board.create('point', [-6,0],{name:'F1',fixed:true, label:{offset:[-40,10]}});
var F2 = board.create('point', [function(){return -F1.X()},function(){return F1.Y();}],{name:'F2',label:{offset:[-20, -15]}});
var p1 = board.create('point', [1,3.5],{name:'',size:0,fixed:true});
var el = board.create('ellipse',[F1,F2,p1],{strokeColor:'red'});
var g1 = board.create('glider', [4.36, 2.76, el],{name:'P'});
//var l1 = board.create('segment', [F1, g1],{strokeWidth:1});
//var l2 = board.create('segment', [F2, g1],{strokeWidth:1});
var x1 =  board.create('point', [1,0],{visible:false});
var x2 =  board.create('point', [5,0],{visible:false});
var cx = board.create('line', [x1,x2],{visible:false});
var y1 =  board.create('point', [0,1],{visible:false});
var y2 =  board.create('point', [0,-1],{visible:false});
var cy = board.create('line', [y1,y2],{visible:false}); 
var i1 = board.create('intersection', [cx, cy],{visible:false});
var vy1 = board.create('intersection', [cy, el],{name:'B',size:0});
var vy2 = board.create('intersection', [cy, el,1],{visible:false});
var vx1 = board.create('intersection', [cx, el],{name:'A',size:0,label:{offset:[0,10]}});
var vx2 = board.create('intersection', [cx, el,1],{visible:false});
var l1 = board.create('segment', [i1, vx1],{strokeWidth:1});
var a = l1.L();
var l2 = board.create('segment', [i1, vy1],{strokeWidth:1});
var b = l2.L(); 
var l3 = board.create('segment', [i1, F1],{strokeWidth:1});
var c = l3.L(); 
var p2 = board.create('point', [a*a/c,0],{visible:false});
var pl1 = board.create('parallel', [cy, p2],{strokeWidth:1});
var l2 = board.create('segment', [F2, vy1],{strokeWidth:1});
var perp1 = board.create('perpendicularsegment', [pl1, vy1],{strokeWidth:1});
var txt1 = board.create('text',[a*a/c+1,0.5,function(){return 'Directrix';}],{display:'internal',rotate:function(){
ang =  90 ; return ang;
}, fontSize:16 });
var txt2 = board.create('text',[a*a/c-4,-5,'x=d'])					

Triangle posted 48 minutes ago

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