7'J 



ANALYTIC GEOMETRY 



[Cm nr, 



increases from to - g (which value it reaches \vli.-n 



* a. - J and then decreases again to 0. The form of tin* 

 curve is therefore as shown in Fig. 85, where OF 



OA 



00 



;, OA' 



(8) The hyperbola, e>l. Equation (1) may also be 

 written in the form 





which, when >1, shows that y is imaginary for all values 



/, /, 



of x between x = - - and x = - , and that y is real for 

 I +e 1 e 



all other values of x. Equation (5) also shows that, as x 



increases from - to oo, y changes from to <x>, ami 

 that, as x decreases from t< oo, y changes from to 

 00. The form of the curve is therefore as shown in 



Fig. 37, where OA = - - and OA' = - 



1-f-e l 



_L_. 

 e I 



Although these three curves differ so widely in form, they 

 are really very closely related as will be further shown in 

 Chap. XII, and in Note D of the Appendix. 



