Solution 2 (a).
See text and/or instructor's solution manual.
Use the relations , and
and polar coordinates , , and
and then get the equations
Solve these equations for , and get
and , respectively.
Use the trigonometric identity to eliminate ,
and obtain the equation of an ellipse
We are done.
Aside. We can let Mathematica double check our work.
We are really done.
Aside. We can graph the images of some circles under the mapping .
image of the circles , (for ), are
mapped onto the ellipses
the ellipses by the Joukowski transformation .
This solution is complements of the authors.
(c) 2008 John H. Mathews, Russell W. Howell