Exercise 3.  Sketch the set of points satisfying the following relations.  

3 (a).  .

Solution 3 (a).

See text and/or instructor's solution manual.

Answer.  The points that lie to the extreme right or left of the branches of the hyperbola  .  

Solution.   The mapping is    and

the point    in the xy-plane is mapped to the point    in the uv-plane,

and we get Equations (2-9);    and  .  

Given that  ,  we conclude that  ,  

which are the points that lie to the extreme right or left of the branches of the hyperbola  .  

                    The set of points satisfying the relation  .   

We are done.   

Aside.  We can let Mathematica double check our work.

                    The set of points satisfying the relation  .   

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell