The auxiliary circle x^{2+y}^2=$a^2$ circumscribes the ellipse. For a point P = (acos(theta), bsin(theta)) on the ellipse, the corresponding point on the auxiliary circle is Q = (acos(theta), asin(theta)). PQ is vertical. The eccentric angle theta is the angle that OQ makes with the positive x-axis. This provides a geometric interpretation of the parametric form.