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Ellipse: pin and string method
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<iframe 
    src="http://jsxgraph.uni-bayreuth.de/share/iframe/ellipse-pin-and-string-method" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Ellipse: pin and string method" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution 4.0 International License.
    https://creativecommons.org/licenses/by/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    JXG.Options.label.autoPosition = true;
    JXG.Options.text.fontSize = 16;
    JXG.Options.line.strokeWidth = 0.8;
    
    const board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-5, 5, 5, -5], 
        axis: true
    });
    
    var f1 = board.create('glider', [-2, 0, board.defaultAxes.x], {name:"f'"});
    var f2 = board.create('glider', [2,  0, board.defaultAxes.x], {name:"f"});
    var ell = board.create('ellipse', [f1, f2, [0,3]]);
    
    var P = board.create('glider', [-1, 2, ell], {name: 'p'}); 
    var s1 = board.create('segment', [f1,P]);
    var s2 = board.create('segment', [f2,P]);
    
    var txt = board.create('text', [0.2, 4, 
        () => "|pf| + |pf'| = " + P.Dist(f1).toFixed(2) + ' + ' +  P.Dist(f2).toFixed(2) + ' = ' + (P.Dist(f1) + P.Dist(f2)).toFixed(2)
    ]);
    
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 16;
JXG.Options.line.strokeWidth = 0.8;

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5], 
    axis: true
});

var f1 = board.create('glider', [-2, 0, board.defaultAxes.x], {name:"f'"});
var f2 = board.create('glider', [2,  0, board.defaultAxes.x], {name:"f"});
var ell = board.create('ellipse', [f1, f2, [0,3]]);

var P = board.create('glider', [-1, 2, ell], {name: 'p'}); 
var s1 = board.create('segment', [f1,P]);
var s2 = board.create('segment', [f2,P]);

var txt = board.create('text', [0.2, 4, 
    () => "|pf| + |pf'| = " + P.Dist(f1).toFixed(2) + ' + ' +  P.Dist(f2).toFixed(2) + ' = ' + (P.Dist(f1) + P.Dist(f2)).toFixed(2)
]);

<jsxgraph width="100%" aspect-ratio="1 / 1" title="Ellipse: pin and string method" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution 4.0 International License.
   https://creativecommons.org/licenses/by/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   JXG.Options.label.autoPosition = true;
   JXG.Options.text.fontSize = 16;
   JXG.Options.line.strokeWidth = 0.8;
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-5, 5, 5, -5], 
       axis: true
   });
   
   var f1 = board.create('glider', [-2, 0, board.defaultAxes.x], {name:"f'"});
   var f2 = board.create('glider', [2,  0, board.defaultAxes.x], {name:"f"});
   var ell = board.create('ellipse', [f1, f2, [0,3]]);
   
   var P = board.create('glider', [-1, 2, ell], {name: 'p'}); 
   var s1 = board.create('segment', [f1,P]);
   var s2 = board.create('segment', [f2,P]);
   
   var txt = board.create('text', [0.2, 4, 
       () => "|pf| + |pf'| = " + P.Dist(f1).toFixed(2) + ' + ' +  P.Dist(f2).toFixed(2) + ' = ' + (P.Dist(f1) + P.Dist(f2)).toFixed(2)
   ]);
   
</jsxgraph>

Ellipse: pin and string method

Analytic
Geometry
Have also a look at the examples
Web references 
// Define the id of your board in BOARDID

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 16;
JXG.Options.line.strokeWidth = 0.8;

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5], 
    axis: true
});

var f1 = board.create('glider', [-2, 0, board.defaultAxes.x], {name:"f'"});
var f2 = board.create('glider', [2,  0, board.defaultAxes.x], {name:"f"});
var ell = board.create('ellipse', [f1, f2, [0,3]]);

var P = board.create('glider', [-1, 2, ell], {name: 'p'}); 
var s1 = board.create('segment', [f1,P]);
var s2 = board.create('segment', [f2,P]);

var txt = board.create('text', [0.2, 4, 
    () => "|pf| + |pf'| = " + P.Dist(f1).toFixed(2) + ' + ' +  P.Dist(f2).toFixed(2) + ' = ' + (P.Dist(f1) + P.Dist(f2)).toFixed(2)
]);

license

This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.