( ii \n i i: iv 



THE EQUATION OF A LOCUS 



42. The equation of a locus. The second fundamental 

 > of analytic georntM .- reverse of the first 



id is usualU in..!.- dilVu-ult. It IB to find, 

 iji-oiurinr iiLjuiv, ..i lonis, tlio corresponding 

 equation, i ,., the r.jii.ii ;..n xvhieh .shall be satisfied by the 

 ties of every point of the given locus, and \\hi.-li 

 isfied by the coordinates of any other point. 

 The ^r.,im-trie liu'im- ma\ !* i;i\en in t\\ \\.i\s. M/. ; 

 As a figure with certain known i>n|)erties; and 

 U tlc path of a point \\huli moves under known 

 litions. 



In tli.- latter case the path is usually unknown, and th<- 

 coni] '>blem is, first to find tin- equation of tlio jMith, 



and thru from this equation to find the properties of 

 In- third problem mentioned in Art 

 The two ways by \vhirh a locus may be "giveo" corre- 



1 to the two conceptions of a locus mentioned in 

 85, and they lead to some what 'InTnvnt method* of obtain 



Illation. The first method may be exemplified .1. 

 and most simply, ly first conoid, ring the familiar cases of 

 -traiU'ht line and tin- . ircle. 



4a Equation of straight line through two given points.* 

 1 P s ==(1_ 5) IH two given point*; and 



61. 



