r; u ; 



TUX EQUATION OF A LOCUS 



/* 3 may alo bo 



an\ i ' on tin- lint- tlir..ni;|i J\ 



seen an follows : 



/ ' < . v t ) 



bo any point ma ..i, (in- 

 line through /', .inl 

 the ordinate M^l\ will 



no.. 



P 4 (r 4 , \\lii.-l 



jr 4 -x s hut y 4 >y r Since P 4 is on the line /VV iu 

 oodrdiuates satisfy equation (1), ili.-i.-fore 



: ^t - ** ~ 8 ^ ; * [nce ar 4 - ar a and y 4 ^ y t ] 

 e the coordinates of 7' 3 do not > >< 



44. Equation of straight line passing through given point 

 and in given direction.! In- tli. ^iv.-n point. 



-.iuiurli /', make an angle of 30 with tin- 

 r-axi, and let /* = (JT, y) >int on this : 



I >niw the ordinates M^\ ami 3fP, and through /*, draw 

 parallel to the j- M 





i . proof shows clearly that if the coordinate* of any point on tho 

 straight line through I\ and P, are substituted for r and y in equation (1) 

 na member will be equal to itro ; if the coordinates of .. Vlow 



me are so subntituted the first member will be negative ; and if the coor- 

 dinates of any point above this line are so substituted the first member will bo 

 positive. This line may then be regarded as the boundary which separate* 

 that part of the plane f,, r which :\y - r - :\ is negative from the pa: 

 whi. ion U positive. Because of this fact that side of thb line on 



> A lies may be called the iMfrtftw tttt, *ad the other the fosftfet <*. 

 t See also Art. 68. 



