A parabola is drawn to pass thru A and B , the ends of a diameter of a given circle of radius a , and to have as directrix a tangent to a concentric circle of radius b ; the axes being AB and a perpendicular diameter , prove that the locus of the focus of the paprabola is

                  x²              +            y²               =               1

        --------------               ----------------

              b²                          b² - a²