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Standard hyperbola with asymptotes
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<iframe 
    src="https://jsxgraph.org/share/iframe/standard-hyperobla-with-asymptotes" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Standard hyperbola with asymptotes" 
    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.line.strokeWidth = 0.8;
    
    const board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-5, 5, 5, -5],
        axis: true
    });
    
    var h = board.create('hyperbola', [
        [-Math.sqrt(2), 0],
        [Math.sqrt(2), 0],
        [2, Math.sqrt(3)]
    ]);
    
    // Asymptotes
    var l1 = board.create('line', [0, 1, 1], {
        dash: 1,
        fixed: true,
    });
    
    var l2 = board.create('line', [0, -1, 1], {
        dash: 1,
        fixed: true,
    });
 </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.line.strokeWidth = 0.8;

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

var h = board.create('hyperbola', [
    [-Math.sqrt(2), 0],
    [Math.sqrt(2), 0],
    [2, Math.sqrt(3)]
]);

// Asymptotes
var l1 = board.create('line', [0, 1, 1], {
    dash: 1,
    fixed: true,
});

var l2 = board.create('line', [0, -1, 1], {
    dash: 1,
    fixed: true,
});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Standard hyperbola with asymptotes" 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.line.strokeWidth = 0.8;
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-5, 5, 5, -5],
       axis: true
   });
   
   var h = board.create('hyperbola', [
       [-Math.sqrt(2), 0],
       [Math.sqrt(2), 0],
       [2, Math.sqrt(3)]
   ]);
   
   // Asymptotes
   var l1 = board.create('line', [0, 1, 1], {
       dash: 1,
       fixed: true,
   });
   
   var l2 = board.create('line', [0, -1, 1], {
       dash: 1,
       fixed: true,
   });
</jsxgraph>

Standard hyperbola with asymptotes

Analytic
Curves
Geometry
Static example of standard hyperbola
// Define the id of your board in BOARDID

JXG.Options.line.strokeWidth = 0.8;

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

var h = board.create('hyperbola', [
    [-Math.sqrt(2), 0],
    [Math.sqrt(2), 0],
    [2, Math.sqrt(3)]
]);

// Asymptotes
var l1 = board.create('line', [0, 1, 1], {
    dash: 1,
    fixed: true,
});

var l2 = board.create('line', [0, -1, 1], {
    dash: 1,
    fixed: true,
});

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.