Elliptical 3D camera orbit- really need help with the math, please

Here’s my issue- I’d have a 3D camera rotating around its target. I want its rotation around the Y-axis (yaw) to be elliptical.

http://www.kevinburkeportfolio.com/ellipse.jpg

I’ve been advised by others to change “The location of the camera over time with a varying distance instead of a static one.” I’m not really sure how to go about this…Any help would be a life-saver.

This is the code for the camera:

Actionscript Code:

public override function orbit(pitch:Number, yaw:Number, useDegrees:Boolean=true, target:DisplayObject3D=null):void
        {
            target = target || _target;
            target = target || DisplayObject3D.ZERO;

            if(useDegrees)
            {
                pitch *= (Math.PI/180);
                yaw *= (Math.PI/90);
            }
           
            // Number3D.sub
            var dx             :Number = target.world.n14 - this.x;
            var dy             :Number = target.world.n24 - this.y;
            var dz             :Number = target.world.n34 - this.z;
           
            // Number3D.modulo
            var distance     :Number = Math.sqrt(dx*dx+dy*dy+dz*dz);

            // Rotations
            var rx :Number = Math.cos(yaw) * Math.sin(pitch);
            var rz :Number = Math.sin(yaw) * Math.sin(pitch);
            var ry :Number = Math.cos(pitch);
           
            // Move to specified location
            this.x = target.world.n14 + (rx * distance);
            this.y = target.world.n24 + (ry * distance);
            this.z = target.world.n34 + (rz * distance);
           
            this.lookAt(target);
        }