Parabola II

The underlying JavaScript code

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 16;
JXG.Options.line.strokeWidth = 0.8;

var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-5, 5, 5, -5], axis: true, showClearTraces: true});

var f = board.create('glider', [1, 0, board.defaultAxes.x], {name:"f"});
var c = board.create('glider', [-1, 0, board.defaultAxes.x], {name:"-c"});
var l = board.create('parallel', [board.defaultAxes.y, c], {name:"l", withLabel:true});

var par = board.create('parabola', [f, l]);

var P = board.create('glider', [2, 2, par], {name: 'p'}); 
var s1 = board.create('segment', [f,P]);

var q = board.create('point', [()=>c.X(), ()=>P.Y()], {name:'q'});
var s2 = board.create('segment', [q, P]);

var txt = board.create('text', [0.2, 4, () => "|pf| - |pq| = " + P.Dist(f).toFixed(2) + ' - ' +  P.Dist(q).toFixed(2) + ' = ' + (P.Dist(f) - P.Dist(q)).toFixed(2)]);