Generate a random point within a circle (uniformly)

Question

I need to generate a uniformly random point within a circle of radius R.

I realize that by just picking a uniformly random angle in the interval [0 ... 2π),

Answer 1

1) Choose a random X between -1 and 1.

var X:Number = Math.random() * 2 - 1;

2) Using the circle formula, calculate the maximum and minimum values of Y given that X and a radius of 1:

var YMin:Number = -Math.sqrt(1 - X * X);
var YMax:Number = Math.sqrt(1 - X * X);

3) Choose a random Y between those extremes:

var Y:Number = Math.random() * (YMax - YMin) + YMin;

4) Incorporate your location and radius values in the final value:

var finalX:Number = X * radius + pos.x;
var finalY:Number = Y * radois + pos.y;