Conic sections: Difference between revisions

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===Ellipse===
The input elements for an ellipse are either
* three points: the two foci and a point on the ellipse
* two point and a number: the two foci and the length of the major axis (maybe a function, too).
<jsxgraph width="600" height="400" box="jxgbox1">
<jsxgraph width="600" height="400" box="jxgbox1">
(function(){
var brd1=JXG.JSXGraph.initBoard('jxgbox1',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var brd1=JXG.JSXGraph.initBoard('jxgbox1',{boundingbox:[-3,3,3,-3], keepaspectratio:true});


Line 6: Line 11:
var C = brd1.create('point',[0,-1]);
var C = brd1.create('point',[0,-1]);
var ell = brd1.create('ellipse',[A,B,C]);
var ell = brd1.create('ellipse',[A,B,C]);
})();
</jsxgraph>
</jsxgraph>
<source lang="javascript">
var brd1=JXG.JSXGraph.initBoard('jxgbox1',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var A = brd1.create('point',[-1,1]);
var B = brd1.create('point',[1,1]);
var C = brd1.create('point',[0,-1]);
var ell = brd1.create('ellipse',[A,B,C]);
</source>


<jsxgraph width="600" height="400" box="jxgbox2">
<jsxgraph width="600" height="400" box="jxgbox2">
(function(){
var brd2=JXG.JSXGraph.initBoard('jxgbox2',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var brd2=JXG.JSXGraph.initBoard('jxgbox2',{boundingbox:[-3,3,3,-3], keepaspectratio:true});


var A = brd2.create('point',[-1,0]);
var A = brd2.create('point',[-1,0]);
var B = brd2.create('point',[1,0]);
var B = brd2.create('point',[1,0]);
var s = brd2.create('slider',[[-1,-2],[1,-2],[0,5,10]]);
var s = brd2.create('slider',[[-1,-2],[1,-2],[0,4,10]]);
var ell = brd2.create('ellipse',[A,B,function(){return s.Value();}]);
var ell = brd2.create('ellipse',[A,B,function(){return s.Value();}]);
})();
</jsxgraph>
</jsxgraph>
<source lang="javascript">
var brd2=JXG.JSXGraph.initBoard('jxgbox2',{boundingbox:[-3,3,3,-3], keepaspectratio:true});


var A = brd2.create('point',[-1,0]);
var B = brd2.create('point',[1,0]);
var s = brd2.create('slider',[[-1,-2],[1,-2],[0,4,10]]);
var ell = brd2.create('ellipse',[A,B,function(){return s.Value();}]);
</source>
===Hyperbola===
The input elements for a hyperbola are either
* three points: the two foci and a point on the hyperbola
* two point and a number: the two foci and the length of the major axis (maybe a function, too).
<jsxgraph width="600" height="400" box="jxgbox3">
<jsxgraph width="600" height="400" box="jxgbox3">
(function(){
var brd3=JXG.JSXGraph.initBoard('jxgbox3',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var brd3=JXG.JSXGraph.initBoard('jxgbox3',{boundingbox:[-3,3,3,-3], keepaspectratio:true});


Line 24: Line 53:
var C = brd3.create('point',[0,-1]);
var C = brd3.create('point',[0,-1]);
var hyp = brd3.create('hyperbola',[A,B,C]);
var hyp = brd3.create('hyperbola',[A,B,C]);
})();
</jsxgraph>
</jsxgraph>
<source lang="javascript">
var brd3=JXG.JSXGraph.initBoard('jxgbox3',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var A = brd3.create('point',[0,1]);
var B = brd3.create('point',[1,1]);
var C = brd3.create('point',[0,-1]);
var hyp = brd3.create('hyperbola',[A,B,C]);
</source>


<jsxgraph width="600" height="400" box="jxgbox4">
<jsxgraph width="600" height="400" box="jxgbox4">
(function(){
var brd4=JXG.JSXGraph.initBoard('jxgbox4',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var brd4=JXG.JSXGraph.initBoard('jxgbox4',{boundingbox:[-3,3,3,-3], keepaspectratio:true});


var A = brd4.create('point',[-1,0]);
var A = brd4.create('point',[-1,0]);
var B = brd4.create('point',[1,0]);
var B = brd4.create('point',[1,0]);
var s = brd4.create('slider',[[-1,-2],[1,-2],[0,0.5,1]]);
var s = brd4.create('slider',[[-1,-2],[1,-2],[0,0.5,3]]);
var hyp = brd4.create('hyperbola',[A,B,function(){return s.Value();}]);
var hyp = brd4.create('hyperbola',[A,B,function(){return s.Value();}]);
})();
</jsxgraph>
</jsxgraph>
<source lang="javascript">
var brd4=JXG.JSXGraph.initBoard('jxgbox4',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var A = brd4.create('point',[-1,0]);
var B = brd4.create('point',[1,0]);
var s = brd4.create('slider',[[-1,-2],[1,-2],[0,0.5,3]]);
var hyp = brd4.create('hyperbola',[A,B,function(){return s.Value();}]);
</source>


===Parabola===
The input elements for a parabola are
* a point and a line: focus and the directrix
<jsxgraph width="600" height="400" box="jxgbox5">
<jsxgraph width="600" height="400" box="jxgbox5">
(function(){
var brd5=JXG.JSXGraph.initBoard('jxgbox5',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var A = brd5.create('point',[-1,1]);
var B = brd5.create('point',[1,1]);
var line = brd5.create('line',[A,B]);
var C = brd5.create('point',[0,-1]);
var par = brd5.create('parabola',[C,line]);
})();
</jsxgraph>
<source lang="javascript">
var brd5=JXG.JSXGraph.initBoard('jxgbox5',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var brd5=JXG.JSXGraph.initBoard('jxgbox5',{boundingbox:[-3,3,3,-3], keepaspectratio:true});


Line 42: Line 104:
var line = brd5.create('line',[A,B]);
var line = brd5.create('line',[A,B]);
var C = brd5.create('point',[0,-1]);
var C = brd5.create('point',[0,-1]);
var hyp = brd5.create('parabola',[C,line]);
var par = brd5.create('parabola',[C,line]);
</source>
 
===Conic section through five points===
<jsxgraph width="600" height="400" box="jxgbox6">
(function(){
var brd6=JXG.JSXGraph.initBoard('jxgbox6',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
 
var A = brd6.create('point',[0.55,0]);
var B = brd6.create('point',[1,1]);
var C = brd6.create('point',[2,-1]);
var D = brd6.create('point',[2,2]);
var E = brd6.create('point',[0.3,-2]);
var con = brd6.create('conic',[A,B,C,D,E]);
})();
</jsxgraph>
</jsxgraph>
<source lang="javascript">
var brd6=JXG.JSXGraph.initBoard('jxgbox6',{boundingbox:[-3,3,3,-3], keepaspectratio:true});
var A = brd6.create('point',[0.55,0]);
var B = brd6.create('point',[1,1]);
var C = brd6.create('point',[2,-1]);
var D = brd6.create('point',[2,2]);
var E = brd6.create('point',[0.3,-2]);
var con = brd6.create('conic',[A,B,C,D,E]);
</source>
[[Category:Geometry]]
[[Category:Examples]]

Latest revision as of 09:12, 13 March 2015

Ellipse

The input elements for an ellipse are either

  • three points: the two foci and a point on the ellipse
  • two point and a number: the two foci and the length of the major axis (maybe a function, too).

var brd1=JXG.JSXGraph.initBoard('jxgbox1',{boundingbox:[-3,3,3,-3], keepaspectratio:true});

var A = brd1.create('point',[-1,1]);
var B = brd1.create('point',[1,1]);
var C = brd1.create('point',[0,-1]);
var ell = brd1.create('ellipse',[A,B,C]);


var brd2=JXG.JSXGraph.initBoard('jxgbox2',{boundingbox:[-3,3,3,-3], keepaspectratio:true});

var A = brd2.create('point',[-1,0]);
var B = brd2.create('point',[1,0]);
var s = brd2.create('slider',[[-1,-2],[1,-2],[0,4,10]]);
var ell = brd2.create('ellipse',[A,B,function(){return s.Value();}]);

Hyperbola

The input elements for a hyperbola are either

  • three points: the two foci and a point on the hyperbola
  • two point and a number: the two foci and the length of the major axis (maybe a function, too).

var brd3=JXG.JSXGraph.initBoard('jxgbox3',{boundingbox:[-3,3,3,-3], keepaspectratio:true});

var A = brd3.create('point',[0,1]);
var B = brd3.create('point',[1,1]);
var C = brd3.create('point',[0,-1]);
var hyp = brd3.create('hyperbola',[A,B,C]);


var brd4=JXG.JSXGraph.initBoard('jxgbox4',{boundingbox:[-3,3,3,-3], keepaspectratio:true});

var A = brd4.create('point',[-1,0]);
var B = brd4.create('point',[1,0]);
var s = brd4.create('slider',[[-1,-2],[1,-2],[0,0.5,3]]);
var hyp = brd4.create('hyperbola',[A,B,function(){return s.Value();}]);

Parabola

The input elements for a parabola are

  • a point and a line: focus and the directrix

var brd5=JXG.JSXGraph.initBoard('jxgbox5',{boundingbox:[-3,3,3,-3], keepaspectratio:true});

var A = brd5.create('point',[-1,1]);
var B = brd5.create('point',[1,1]);
var line = brd5.create('line',[A,B]);
var C = brd5.create('point',[0,-1]);
var par = brd5.create('parabola',[C,line]);

Conic section through five points

var brd6=JXG.JSXGraph.initBoard('jxgbox6',{boundingbox:[-3,3,3,-3], keepaspectratio:true});

var A = brd6.create('point',[0.55,0]);
var B = brd6.create('point',[1,1]);
var C = brd6.create('point',[2,-1]);
var D = brd6.create('point',[2,2]);
var E = brd6.create('point',[0.3,-2]);
var con = brd6.create('conic',[A,B,C,D,E]);
Retrieved from "http://jsxgraph.org/wiki/index.php?title=Conic_sections&oldid=6393"