Mi] //// / v or A LOCUS ;: 



JT'-VCs-Ty+V 



/ / ' [algebraic equivalents] 



banoe V(*- *)* + y-, 



(l-it)!*** 1 ---'*'**-*), (1, 



h IN tin* r.ju.ition of the given locos. 



;i is of the. Kceond degree; in a later chapter 

 ill be shown that every equation of the second degree 

 between two variables represents a conic section. On 

 account it is often spoken of as the "second degree curve/* 



Ditrutsion of equation ( 1 



If x a 0, then y=s4rV~l, \\liirhshows that this on 

 does not intersect tin* y-nxis as here chosen; i.e., a conic 

 does not intersect its di: 



If y - 0, then (1 - e*)# - 2kx + ** = 0, 

 whence *a-^-, or x= p , . . 



a conic meets the line drawn through the focus and per- 

 pendicular to the directrix (the ar-axis as here chosen) in 

 two points whose distances from the directrix are - - and 



k ! + e 



j-^- respect i\rl\ ; these points are called the vertices of il*- 



nation (1) shows that for every value of r, the 

 s[>on<ling values of y are numerically equal but of 

 site signs, hence the conic is > <-al with regard 



to t)ic jr-axis as here chosen. For this reason the INK- 

 .n through the focus of a conic and perpendicular to 

 the <-d the principal axis of the com. . 



i of the locus of equation (1) depends upon the 

 ." of the eccent :" e = 1, the conic is called a 



