Trochoid

The Trochoid curve (blue) and its dual curve (red). The equation of the trochoid is

$x = a\phi-b\sin(\phi)$
$y = a-b\cos(\phi)$

The underlying JavaScript code

<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>
<script language="JavaScript">
board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
board.suspendUpdate();
var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
var x = function(phi) { return a.Value()*phi-b.Value()*Math.sin(phi); }
var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
var c1 = board.createElement('curve', [x,y,-Math.PI*4,Math.PI*4],{strokeWidth:3});

var dualCurve = function(x,y,board) {
var X = function(phi) { return board.D(y)(phi)/(y(phi)*board.D(x)(phi)-x(phi)*board.D(y)(phi)); }
var Y = function(phi) { return board.D(x)(phi)/(x(phi)*board.D(y)(phi)-y(phi)*board.D(x)(phi)); }
return [X,Y];
}
var dual = dualCurve(x,y,board);
var c2 = board.createElement('curve', [dual[0],dual[1],-Math.PI*1,Math.PI*1],{strokeWidth:3, strokeColor:'red'});
board.unsuspendUpdate();
</script>