N AXAL\ //' 



EXERCISES 



What loci are represented by the following equations? 

 l.jrjr = 0. 2. * V- = 0. 3. 



'y-2r*y = 0. 3. jr*-2x+l = 0. 6. 



41. Locus represented by the sum of two equations. Sup- 

 pose the equations 

 2y-z = . . . (1), and y-x=0 ... (2) 



are given. Their loci are respectively AB and DP 2 1\<' 



(Art. :'.'.), and it is required to find the locus of their MUM ; 



or, what is the same thin 

 2z = . . . 



The locus of this last equa- 

 tion passes through all the 

 points in which An and 

 intersect each other. 

 For let P\=(Xvy\) be one <>i 

 these points, then since P, 

 'ii AB, its coordinates satisfy equation (1); i.e., 



and since P l lies on DP^P V C, its coordinates satisfy equa 



lions ( '1)\ i.e., 



yf-Xi-Ol . . . 



therefore, by adding equations (4 ) and (5), 



This last equation proves (Art. 35 ( 1 j ) that P l = (x v v,> 

 is on the locus of equation (3); i.e., the locus of equation 

 (3) passes through P l ==(x l , y^. 



Similar reasoning would show that the locus of equation 



r 



Kio.28. 



