Math trouble ! Help !

Question

I try to calculate all the points on a curve.
The curve decided by the width(X on the picture) and height(Y on the picture) properties of a movieclip.
The distance between each green point on curve is the same.

Answer 1

I think dealing with ellipse or bezier in this context is too cumbersome and pretty imprecise.
Code below accomplished drawing interface you want and positions point at equal intervals along the curve.Just make this class a document class.
Read comments:
package
     import flash.display.GradientType;
     import flash.display.Graphics;
     import flash.display.Sprite;
     import flash.geom.Matrix;
     public class ObjectCurve extends Sprite
          private var container:Sprite;
          // container width
          private var w:Number = 500;
          // container height
          private var h:Number = 400;
          // reusable Graphics reference
          private var g:Graphics;
          public function ObjectCurve()
               init();
          private function init():void
               // make container
               container = new Sprite();
               g = container.graphics;
               with (g) {
                    beginFill(0xEBEBEB);
                    drawRect(0, 0, w, h);
                    endFill();
               container.x = container.y = 50;
               addChild(container);
                * diagonal is base of right triangle that is made of
                * two radiuses
                * IMPORTANT! Center of cricle is positined at x = width of container
                * and y = radius.
                * radius is most important value to calculate fro this functionality
                * it depends on, again, container dimensions
               // length of container diagonal
               var diagonal:Number = Math.sqrt(w * w + h * h);
               // angle of container diagonal
               var diagonalAngle:Number = Math.atan2(h, -w);
               // radius of the circle which will be used for calculating anlges.
               var radius:Number = diagonal * .5 / Math.sin(diagonalAngle);
               // angle between left buttom corner of container and center of circle
               var angle:Number = Math.atan2(h - radius, -w);
               // angle between radiuses
               var radAngle:Number = -(angle - ( -90 * Math.PI / 180));
               // length of arc that will be drawn
               var arcLength:Number = radAngle * radius;
               // radian increment for each roation
               var rotationIncrement:Number = radAngle * 4 / arcLength;
               // prepare for gradiwnt fill
               var matrix:Matrix = new Matrix();
               matrix.createGradientBox(w, h, -45 * Math.PI / 180);
               var colors:Array = [0x000000, 0x4646FF];
               var alphas:Array = [1, 1];
               var ratios:Array = [0x00, 0xFF];
               // draw arc
               g = container.graphics;
               g.lineStyle(2, 0xFFFF00);
               g.beginGradientFill(GradientType.LINEAR, colors, alphas, ratios, matrix);
               g.moveTo(0, h);
               while (angle < -90 * Math.PI / 180) {
                    g.lineTo(w + radius * Math.cos(angle) , radius + radius * Math.sin(angle));
                    angle += rotationIncrement;
               // finish to top right corner
               g.lineTo(w, 0);
               // continue drawing to make borders
               g.lineTo(w, h);
               g.lineTo(0, h);
               // place points at equal intervals
               // number of points
               var numPoints:int = 10;
               // number of segments based on number of points
               rotationIncrement = radAngle / numPoints;
               // return angle to its original value
               angle = Math.atan2(h - radius, -w);
               var point:Sprite = drawPoint();
               // place first point at the beginning of arc
               point.x = w + radius * Math.cos(angle);
               point.y = radius + radius * Math.sin(angle);
               container.addChild(point);
               // create and place other points
               for (var i:int = 0; i < numPoints; i++) {
                    angle += rotationIncrement;
                    point = drawPoint();
                    point.x = w + radius * Math.cos(angle);
                    point.y = radius + radius * Math.sin(angle);
                    container.addChild(point);
          private function drawPoint():Sprite {
               var s:Sprite = new Sprite();
               s.graphics.beginFill(0x00FF00);
               s.graphics.drawCircle(0, 0, 5);
               return s;