Why and How the plot between the real and imaginary component of an analytic signal is in the form of an ellipse pattern ?

Why and How the plot between the real and imaginary component of an analytic signal is in the form of an ellipse pattern ? How does the ellipse pattern varies with the variation in real and imaginary components of an analytic signal ? Can you share a research paper (journal or conference paper) to study more about it ? Because I am also working in this area of research.