.: ; TIIK UTRAl'.Hl /-/.VJT UN 



A.V. Let line (1) make an angle t , line (2) an angle 

 $ v and LM AI\ angle r with the x-axis ; then 



f-^-*,, and 180- *-,-',. 



ii gives 



l _ 



' 



In these equations <f> and f are known, hence tantf, an- 1 



tan0 t can be found. II ud tan0, and tan 0, the 



equations of lines (1) and (2) may at once be written down, 



r by means of equation [ i j, or o\ the method employed 



EXERCISES 



1 1 1 the equations of the two linen which pas* through the point 

 (ft, 8), and each of which make* an angle of 45 with tin ! y =6. 



2. Show that the equations of the two straight lines pawing through 

 the point (3, ->) and inclined atOO^to the line 



the equation of the straight line 



S. making an angle of +? with the line 3x- 4y = 7; construct the 

 Why is there an undetermined constant in the resulting equation? 



4. making an angle of - 60 with the line 5 x + 12y + 1 = 0; con- 

 the figure. 



5. making an angle of + 30 with the line r-2y+l=0, and 



through the point (!.:'.): making an angle of 30, and 

 the same point. 



making an angle of 135 with the line r + f = 2, and 

 the origin. 



. making the angle tan~( - *\ with the line ^ -f J = 1, and passing 

 th, ; ;). 



8. Find t)i ..... | nation of a line through the ; ) form in 



KINM 2x-^ + a = o and ay-f 6x = 7 a rightangled triangle. Kind 

 TertioM of the triangle (twosuluti 



