JSFiddle - React, Tailwind, and code Playground

HTML

<div id="inputs" style="position:absolute;">
  <div>
    1 point:
    <input type="text" disabled />
    <input type="text" disabled />
  </div>
  <div>
    2 point:
    <input type="text" disabled />
    <input type="text" disabled />
  </div>
  <div>
    3 point:
    <input type="text" disabled />
    <input type="text" disabled />
  </div>
  <div>
    4 point:
    <input type="text" disabled />
    <input type="text" disabled />
  </div>
  <div>
    5 point:
    <input type="text" disabled />
    <input type="text" disabled />
  </div>
  <br />
  <div id="info-x"></div>
  <div id="info-y"></div>
  <div id="info-r1"></div>
  <div id="info-r2"></div>
  <div id="info-rotation"></div>
  <br / >
  <div id="info-ca"></div>
  <div id="info-cb"></div>
  <div id="info-cc"></div>
  <div id="info-cd"></div>
  <div id="info-ce"></div>
  <div id="info-cf"></div>
</div>
<canvas id="canvas" style="width:100%;height:100%;"></canvas>

CSS

body,
html {
  width: 100%;
  height: 100%;
}

input {
  width: 40px;
}

JavaScript

var offset = 400;

var Points = [
  [offset + 200, offset + 100], // x, y
  [offset + 100, offset + 100],
  [offset + -200, offset + -200],
  [offset + -100, offset + -200],
  [offset + 100, offset + -100]
];

// You can remove the comment is for visualization. In this case, all is well
/*
var Points = [
  [280, 260],
  [315, 330],
  [520, 285],
  [360, 165],
  [405, 180]
];
*/


// START! :)
Main = function() {
  // get coefficients
  var conic = MyMath.getConicEquationFromFivePoints(Points);

  // **************************************************
  
  var A = conic[0];
  var B = conic[1];
  var C = conic[2];
  var D = conic[3];
  var E = conic[4];
  var F = conic[5];

  // the center is located at
  var xc = (B * E - 2 * C * D) / (4 * A * C - Math.pow(B, 2));
  var yc = (B * D - 2 * A * E) / (4 * A * C - Math.pow(B, 2));
  var Fs = F + ((D * (B * E - C * D) - A * Math.pow(E,2)) / (4 * A * C - Math.pow(B,2)));
  
  // The polar distance at angle θ is found by rotation of the axes. The major and minor axes are
  var R1 = Math.sqrt((-2 * Fs) / (A + C - Math.sqrt(Math.pow(B,2) + Math.pow((A - C),2))));
  var R2 = Math.sqrt((-2 * Fs) / (A + C + Math.sqrt(Math.pow(B,2) + Math.pow((A - C),2))));
  
  // The rotation angle is then found by
  //var Rotation = 1/2 * Math.atan(B/(A-C)); // Old
  
  // It's WORK!)))))) :)
  var Rotation = Math.atan(((C-A)/B) + (Math.sqrt( Math.pow(A-C, 2) + Math.pow(B,2) ) / B));
  

  var Deg = Rotation * (180/Math.PI);
  
  // **************************************************
  
  // draw ellipse
  Canvas.ellipse(xc, yc, R2, R1, Rotation, 'rgba(0, 255, 0, 0.4)');
  
  // draw center point
  Canvas.arc(xc, yc, 2);
  
  // draw info
  $('#info-x').text('X center: ' + xc.toFixed(4));
  $('#info-y').text('Y center: ' + yc.toFixed(4));
  $('#info-r1').text('Minor axes: ' + R1.toFixed(4));
  $('#info-r2').text('Major axes: ' + R2.toFixed(4));
  $('#info-rotation').text('Rotation: ' + Rotation.toFixed(4) + ' (' + Deg.toFixed(2) + '°)');
  
 ...