The Imaginary in Geometry 



47 



By parallel projection we get the hyperbolas 



2 2 



a 2 b 2 l ' 



Notice, however, that the projections of the foci will not be the 

 foci of the projected curve. These latter are on 



x 2 -f- y 2 = # 2 + b 2 , 

 Y 



Fig. 43. 



or are terminated by that. 

 Figure 44 shows the ellipse 



12 



x y 



\2 ' 71 1 *\2 == 1 » 



a special case of 



(2+2i) 2 ' {l+if 



a 



47 



