Example 2.24.  Consider the mapping  .   
(a)  Find the images of the vertical lines  x = a.   (b)  Find the images the horizontal lines  y = b.  

Explore Solution 2.24.

(a)  First, find the images of the vertical lines  x = a.

The image of the vertical lines  x = a  is the circle,  with center    and radius  .  

(b)  Second, find the images the horizontal lines  y = b.

The image is the circle,  with center    and radius  .  

Now prepare some horizontal and vertical lines in Mathematica for graphing.

Now prepare the image circles in Mathematica for graphing.

Graph the horizontal and vertical lines and their images.

We see that the images of the vertical lines  x = a  and  horizontal lines  y = b  under the mapping   are circles.

(c) 2006 John H. Mathews, Russell W. Howell