Conic sections in polar form

Jump to navigationJump to search

The equation of the curve is

$\, r = \frac{p}{1-\epsilon\cdot cos(\phi+\rho)};$

The JavaScript code to produce this picture

<jsxgraph board="brd" width="600" height="500">
var brd = JXG.JSXGraph.initBoard('jxgbox',{axis:true,originX:300,originY:250,unitX:25,unitY:25});
var p = brd.createElement('slider',[[2,8],[6,8],[0,3,6]]); brd.createElement('text',[1,8,'p:']);
var eps = brd.createElement('slider',[[2,7],[6,7],[-6,0.5,6]]); brd.createElement('text',[1,7,'&epsilon;:']);
var len = brd.createElement('slider',[[2,6],[6,6],[0,3,6]]); brd.createElement('text',[1,6,'len:']);
var rho = brd.createElement('slider', [[2,5],[6,5],[0,0,2*Math.PI]]); brd.createElement('text',[1,5,'&rho;:']);
var f = brd.createElement('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(&phi;+"+(rho.Value()).toFixed(1) +"))";});
</jsxgraph>