I-:..] 





171 



ni, tin ii tho fixed -ailed an asymptote of the 



ly, tliough leaa accurately, this defini- 



may be stated as follows: 



an asymptote to a curve is a 



tangent whoso point of contact 



if at infinity, l.ui \\lmh is not 



nity, It is 



that to have an aaymp- 

 imist have an imi- 

 .:u-h ; ami this In. 



isidered as having 

 two coin. M.-nt, and infinitely 



intersection \\ith its asymptote. Thin 

 I in obtaining the equation of the asymptote. 



ilit'lino y f/w? -f <r, 



in two points whose abscissas are given by the equation 



(oW-fl*)** 4- 2 a'cmx + a'P + aV 0. . . (8) 



If 1 is an asymptote, the two roots of equat 



must both become infinite ; therefore, l.y Art. 10, 



aW-^-O and 2a j cm-0, . . . 

 too. .-0 .n,l if 



Substituting these values in equation ( 2), gives 



y = - r, antl y = - 



(6) 



Thb definition Implk* that 

 MyroploCe becomes inftniu-ly small, 

 cxilas Chaj XIV. 



OBOM. 18 



between a curve and iu 

 4 Snyder, Diflerential Cat- 



