JSXGraph
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Limacon
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<iframe 
    src="https://jsxgraph.uni-bayreuth.de/share/iframe/limacon" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Limacon" 
    allowfullscreen
></iframe>
This code has to 
<button onClick="clearTrace()">Clear Trace</button>

<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 ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    var board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-2, 16, 18, -2], keepaspectratio: true});
    
    var p3 = board.create('point', [8, 4], {face:'x',size:3,name:"P_{3}",fixed:true});
    var p4 = board.create('point', [8, 8], {size:4,face:'x',name:"P_{4}",fixed:true});
    var c1 = board.create('circle', [p4, p3]);
    
    var p6 = board.create('glider', [0, 0, c1], {face:'o',size:5,name:"drag me"});
    var g = board.create('line', [p3, p6]);
    
    var c2 = board.create('circle', [p6, 3]);
    
    var p14_1 = board.create('intersection', [c2,g,0], {size:3,face:'[]',name:"M",trace:true});
    var p14_2 = board.create('intersection', [c2,g,1], {size:3,face:'[]',name:"N",trace:true});
    
    function clearTrace() {
        p14_1.clearTrace();
        p14_2.clearTrace();
    }
    clearTrace();
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/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!

var board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-2, 16, 18, -2], keepaspectratio: true});

var p3 = board.create('point', [8, 4], {face:'x',size:3,name:"P_{3}",fixed:true});
var p4 = board.create('point', [8, 8], {size:4,face:'x',name:"P_{4}",fixed:true});
var c1 = board.create('circle', [p4, p3]);

var p6 = board.create('glider', [0, 0, c1], {face:'o',size:5,name:"drag me"});
var g = board.create('line', [p3, p6]);

var c2 = board.create('circle', [p6, 3]);

var p14_1 = board.create('intersection', [c2,g,0], {size:3,face:'[]',name:"M",trace:true});
var p14_2 = board.create('intersection', [c2,g,1], {size:3,face:'[]',name:"N",trace:true});

function clearTrace() {
    p14_1.clearTrace();
    p14_2.clearTrace();
}
clearTrace();

Limacon

Curves
With JSXGraph elements can be traced to visualize constructed loci.
Web references 
<button onClick="clearTrace()">Clear Trace</button>
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID, {boundingbox: [-2, 16, 18, -2], keepaspectratio: true});

var p3 = board.create('point', [8, 4], {face:'x',size:3,name:"P_{3}",fixed:true});
var p4 = board.create('point', [8, 8], {size:4,face:'x',name:"P_{4}",fixed:true});
var c1 = board.create('circle', [p4, p3]);

var p6 = board.create('glider', [0, 0, c1], {face:'o',size:5,name:"drag me"});
var g = board.create('line', [p3, p6]);

var c2 = board.create('circle', [p6, 3]);

var p14_1 = board.create('intersection', [c2,g,0], {size:3,face:'[]',name:"M",trace:true});
var p14_2 = board.create('intersection', [c2,g,1], {size:3,face:'[]',name:"N",trace:true});

function clearTrace() {
    p14_1.clearTrace();
    p14_2.clearTrace();
}
clearTrace();

license

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