Conic sections in polar form

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The equation of the curve is

[math]\, r = \frac{p}{1-\epsilon\cdot cos(\phi+\rho)};[/math]


 

The JavaScript code to produce this picture

var brd = JXG.JSXGraph.initBoard('jxgbox',{axis:true,boundingbox: [-12, 10, 12, -10]});
var p = brd.create('slider',[[2,8],[6,8],[0,3,6]]); brd.createElement('text',[1,8,'p:']);
var eps = brd.create('slider',[[2,7],[6,7],[-6,0.5,6]]); brd.createElement('text',[1,7,'ε:']);
var len = brd.create('slider',[[2,6],[6,6],[0,3,6]]); brd.createElement('text',[1,6,'len:']);
var rho = brd.create('slider', [[2,5],[6,5],[0,0,2*Math.PI]]); brd.createElement('text',[1,5,'ρ:']);
var f = brd.create('curve', 
   [function(phi) { return p.Value()/(1-eps.Value()*Math.cos(phi+rho.Value())); }, [1,0], 0,function(){return len.Value()*Math.PI}],      
   {curveType:'polar', strokewidth:2, strokeColor:'#CA7291'}
  );        
var q = brd.createElement('glider', [f], {style:6,name:'G'}); 
brd.createElement('tangent', [q], {dash:3}); 
brd.addHook(function(){document.getElementById('ausgabe').innerHTML = (p.Value()).toFixed(1) + "/(1 - (" + (eps.Value()).toFixed(1) + ")*cos(φ+"+(rho.Value()).toFixed(1) +"))";});