The dark blue line has a length of 1, and always "rests" against the axes of the cartesian coordinate system. The locus of a point at a distance of p along the line, which you can change using the slider, is an ellipse with the equation (py/(1-p))^2+x^2=p^2, and the red curve, which entirely contains the loci of all points on the line has the equation x^(2/3)+y^(2/3) = 1.
Use the right and left arrow keys to change the angle of the dark blue line segment.
