Difference between revisions of "Conic sections in polar form"

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(New page: <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],...)
 
 
(15 intermediate revisions by 2 users not shown)
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The equation of the curve is
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:<math>\, r =  \frac{p}{1-\epsilon\cdot cos(\phi+\rho)};</math>
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 +
 +
<html>
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<p id="ausgabe">&nbsp;
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</p>
 +
</html>
 
<jsxgraph board="brd" width="600" height="500">
 
<jsxgraph board="brd" width="600" height="500">
var brd = JXG.JSXGraph.initBoard('jxgbox',{axis:true,originX:300,originY:250,unitX:25,unitY:25});
+
var brd = JXG.JSXGraph.initBoard('jxgbox',{axis:true,boundingbox: [-12, 10, 12, -10]});
var p = brd.createElement('slider',[[2,8],[6,8],[0,3,6]]); brd.createElement('text',[1,8,'p:']);
+
var p = brd.create('slider',[[2,8],[6,8],[0,3,6]]); brd.createElement('text',[1,8,'p:']);
var eps = brd.createElement('slider',[[2,7],[6,7],[0,2,6]]); brd.createElement('text',[1,7,'&epsilon;:']);
+
var eps = brd.create('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:']);
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var len = brd.create('slider',[[2,6],[6,6],[0,2,6]]); 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;:']);
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var rho = brd.create('slider', [[2,5],[6,5],[0,0,2*Math.PI]]); brd.createElement('text',[1,5,'&rho;:']);
var f = brd.createElement('curve',  
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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}],       
 
   [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'}
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   {curveType:'polar', strokewidth:2, strokeColor:'#CA7291'}
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  );       
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var q = brd.create('glider', [f], {style:6,name:'G'});
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brd.create('tangent', [q], {dash:3});
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brd.addHook(function(){document.getElementById('ausgabe').innerHTML = (p.Value()).toFixed(1) + "/(1 - (" + (eps.Value()).toFixed(1) + ")*cos(&phi;+"+(rho.Value()).toFixed(1) +"))";});
 +
</jsxgraph>
 +
 
 +
===The JavaScript code to produce this picture===
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<source lang="javascript">
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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,'&epsilon;:']);
 +
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,'&rho;:']);
 +
var f = brd.create('curve',
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  [function(phi) { return p.Value()/(1-eps.Value()*Math.cos(phi+rho.Value())); }, [1,0], 0,function(){return len.Value()*Math.PI}],     
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  {curveType:'polar', strokewidth:2, strokeColor:'#CA7291'}
 
   );         
 
   );         
 
var q = brd.createElement('glider', [f], {style:6,name:'G'});  
 
var q = brd.createElement('glider', [f], {style:6,name:'G'});  
 
brd.createElement('tangent', [q], {dash:3});  
 
brd.createElement('tangent', [q], {dash:3});  
</jsxgraph>
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brd.addHook(function(){document.getElementById('ausgabe').innerHTML = (p.Value()).toFixed(1) + "/(1 - (" + (eps.Value()).toFixed(1) + ")*cos(&phi;+"+(rho.Value()).toFixed(1) +"))";});
 
+
</source>
 
 
 
 
 
 
 
 
 
 
 
 
 
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Curves]]
 
[[Category:Curves]]

Latest revision as of 14:56, 7 June 2011

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,'&epsilon;:']);
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,'&rho;:']);
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(&phi;+"+(rho.Value()).toFixed(1) +"))";});