N. 



//// Ihl 



FO-cu. 



cu* Filth* point (- a*. Q). . (2) 



r any po.nt /' .<, draw ih- . 



/. /' the directrix ; then 



/'/' A/', [geometric e<|uat ion] . . 



= Vi JT -- 



*)* + /- 



(1- 

 a' 



(6) 



a equation (6), the intercepts of the curve on the y-axi* 

 are a VI *. H >t h intercepts are real, since e < 1 ; hence 

 the ellipse cuts the y-axis in two real points, B and /?, on 



site sides of the origin and equidistant from it. If 

 OB is denoted by + 6, so that 



a* - 



:ion (6) takes the form 



I.- 



(7) 



[44] 



is the simplest equation ,.f the rllipee, and will IK; 

 used in the subsequent study of the properties of that 

 As will lie seen in Chapter XII, every equation 

 inn- an llipae can be reduced to this form. 



a = 6 (>., If = 0) thb equation 



the circle aa a special 

 whose eccentricity U 



a drde. The dlipee, 

 words: a circle U an 



