You need to build up a list of the points that the circle as been to. Then in your Paint event handler, rather than just drawing the ellipse at x1, y1, you loop around all of the points drawing an ellipse at each....
Code:
// class members
private List<Point> _points = new List<Point>();
private Int32 _x = 50;
private Int32 _y = 50;

// paint handler

Graphics graphics = e.Graphics;

foreach (Point point in _points)
    graphics.FillEllipse(Brushes.Blue, point.X, point.Y, 20, 20)

// in your process command...
if (input == "Down")
{
    _y += 10;
    
    // add the new point to the list
    _points.Add(new Point(_x, _y);

    // ... as before
}
You can now also easily implement a [Shake] button by simply calling:

_points.Clear();

and then refreshing....