TT1K LOCUH OF A.\ KQUAT 



.... 



factor containing the variable*. 1 Ins J.PM!U. t -A ill vini*h if, 

 ami onl <<*ond factor vanished ; Imt tin* fartor will 



:. tin* \ariuhli-s \\hn-h ji 



ii tbo loouji of the original equat 

 lie coordinates of all j*. . of tin- 



no! only tl. . i lmute,8atinfy thoequa 

 it han been umltipli.-'! 1>\ k\ heneo the locti* remain* 

 hanged if iU equ inulti|>lii-<l l\ a tinito constant. 



39. Points of intersection of two loci. Sin<><> t! * of 



iiihTMTtiiin f t\\<. liM-i .11. on each loutm, tlierefore 



t<s of tlu-H4- (Hiinu must satisfy each of tin? two 



equations ; moreover, the coordinates of no other j.mts can 



aatbfv l-th iMjuations. Ilfiuv, to liinl tin- rM.nlin.il-> ol 



I.., mts of intersection of t\\o < . is only necessary to 



reganl their etjimtions as simultaneous and solve for 

 coordinates, 



.1 ili.. c.K>r.liuatA of the point* of intersection, P, and P r of 

 the loci of x - 2y = 0, and y 5 = x. The point of intersection />, = (r,. y,) 

 is on loth curvet, 



r, o. ,, r 1. and y, = 



') are 





i 



twop - of which 



thm-fop- th-y are the j 



of the loci of these 



EXERCISES 



. 1 1,- |H.J!itA of intersection of the following pairs of curves: 

 11 jr + 1 =0, 9 <x-.jr=s, 



A 



If z and y are regarded as the 

 the subscript* may be omiUed ban. 



of the point of interne-Una, 



