Conic sections: Difference between revisions
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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> | ||
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var C = brd5.create('point',[0,-1]); | var C = brd5.create('point',[0,-1]); | ||
var par = brd5.create('parabola',[C,line]); | var par = brd5.create('parabola',[C,line]); | ||
var radpoint = C; | |||
var reflectionpoint = brd5.create('glider',[-7,1,par],{name:'point of reflection'}); | |||
var dir = brd5.create('segment',[radpoint,reflectionpoint],{strokeWidth:1}); | |||
var infty = brd5.create('point', | |||
[ | |||
function(){ | |||
var a = dir.stdform[1], b = dir.stdform[2], | |||
t = reflectionpoint.position, | |||
u = JXG.Math.Numerics.D(par.X)(t), | |||
v = JXG.Math.Numerics.D(par.Y)(t), | |||
dirx = a*v*v-2*b*u*v-a*u*u, | |||
diry = b*u*u-2*a*u*v-b*v*v; | |||
return [0, diry, -dirx]; | |||
} | |||
],{name:'', visible:false}); | |||
var reflection = brd5.create('line', | |||
[reflectionpoint,infty], | |||
{strokeWidth:1, straightFirst:false, trace:true}); | |||
})(); | })(); | ||
</jsxgraph> | </jsxgraph> | ||
Revision as of 16:06, 14 January 2011
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],[0,0.5,1]]);
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]);
