Rectangles in the {Perimeter, Area} plane

Every point in the first quadrant of {width,height plane} corresponds to a rectangle. The applet allows you to generate either a family of rectangles by moving the GOLD point along a height = constant/width curve or a family of rectangles by moving a GOLD point along a height+width = constant curve. [You can position each of these curves by dragging the small WHITE dots.] Can you explain the nature of the curves generated in the {Perimeter, Area} plane as you drag the GOLD dots in the {width, height} plane? qualitatively? analytically? What questions would/could you put to your students based on this applet? What have you learned from this applet?