Show that the joukowski transformation maps a circle at the

Question

Question: 1. Show that the Joukowski transformation maps a circle at the origin in the Z-plane of radius ½(a +b) into an ellipse of semi-axes a, b in the z-plane, given the parameter relation c² = a² - b².

2. Find the critical points of the Joukowski transformation, and (using local polar coordinates) investigate the character of the transformation in the neighborhood of the singular point.