An ellipse in porlar coordinates

						JXG.Options.text.useKatex = true;
JXG.Options.axis.ticks.majorHeight = 10;
JXG.Options.axis.ticks.insertTicks = false;
JXG.Options.axis.ticks.ticksDistance = 100;
var board = JXG.JSXGraph.initBoard('box1', {
boundingbox:[-10, 10, 10, -10],showNavigation:false, showcopyright: false, axis: false,

 var F1 = board.create('point', [-6,0],{name:'F1',size:1, fixed:true, label:{offset:[-40,10]}});
var F2 = board.create('point', [function(){return -F1.X()},function(){return F1.Y();}],{name:'F2',size:1, label:{offset:[15, 10]}});
var p1 = board.create('point', [1,3],{name:'',size:0,fixed:true});
var el = board.create('ellipse',[F1,F2,p1],{strokeColor:'red'});
var g1 = board.create('glider', [2.0, 1.5, el],{name:'P',size:1});
var l1 = board.create('arrow', [F1, g1],{strokeWidth:1});
var l2 = board.create('arrow', [F2, g1],{strokeWidth:1});
var p2 = board.create('point', [function(){return F1.X()}, 2.0],{visible:false});
var l3 = board.create('axis', [F1, p2]);  
var l3 = board.create('axis', [F1, F2]);  
var a1 = board.create('angle', [F2, F1, g1],{name:'θ', radius:2,label:{offset:[5,12]}});
var txt1 = board.create('text',[4,-1,function(){return '2c';}])
var txt2 = board.create('text',[-2,2.1,function(){return 'r';}])					

The image appears in the following posts

  1. An ellipse is a regular oval shape that could be seen in our daily life, ellipse-shaped furniture, architecture or artworks. The earth rotates around the sun in an orbit that is not purely circular, but an elliptical one with an eccentricity of about 0.0167. Ellipse has been studied by mankind for thousands of years.


    History of conic sections

    As one of conic sections, ellipse could be traced back to Ancient Greece. It is believed that the first definition of a conic section was given by Menaechmus ( - 320 BC) as part of his effort to solve the Delian problem (Duplicating the cube). Menaechmus‘ definition lies in slicing a right circular cone with a plane that is orthogonal to the side of the cone. The conic section is the intersecting curve formed on the surface of the cone. It was found that the type of the conic section is dependent on the opening angle of the cone. If the angle is acute then it is an ellipse; if the angle is right then it is a parabola; and if the angle is obtuse then the conic section is a hyperbola.

    Menaechmus' breakthrough left clue for discovery of later mathematicians. Apollonius of Perga (262 BC - 190 BC), known as The Great Geometer, made great advancement in the study of conics. Apollonius's study shows that any plane cutting a right circular cone, no matter its angle is orthogonal or not, will produce a conic section. The difference is the type of the conic. If the angle is less than the opening angle of the cone, the conic section will be ellipse. If the angle is equal to the opening angle of the cone, the conic section will be a parabola. If the angle is larger than the opening angle of the cone, the conic section will be a hyperbola. Apollonius gave the names ellipse (acutangle conic), parabola (rightangle conic) and hyperbola (obtusangle conic) for these curves, which we know today.

Triangle posted 1 day ago

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