63-64) -./// y./.VJT 



16. Do the lines 2x + 3y = 13. 5x - y = 7, and * I y + 10 

 meet in a common poii it are the angles they make with each 



..th.-i ' 



17 I :i>d the angles of the triangle of exercfce 1<X 

 10 u i, a are the lines 



x + (a + 6)y + c SB and (* -f ay) + 6 (x - Ay) + d = 

 parallel? when perpendicular? 



19 rin.l the value of /> for each of the two parallel lines 



y = 3x + 7 and y = 3x - 5; 



and hence And the distance between these lines [of. Art 58 (3) and (4)]. 

 20. What is the distance between the two parallel lines 



5x-3y + 6 = and 6y - lOx = 7? 

 21 Kin.l the cosine of the angle between the lines 



22. What relation exists between the two lines 

 y = 3x + 7 and y = -3x-3? 



23 Kind the angle between the two straight lines 3x = 4y + 7 and 

 5y SB r.'x + 6; and also the equations of the two straight lines u 

 pass through the point (4, 5) and make equal angles with the two given 



MS. 



24. Km.! the angle between the two lines 



3x + y +1L'- and x + 2y - 1 = a 



also the coonlinat intersection, and the equations 



the lines drawn perpendicular to them from the point (3, 



I 



64. The distance of a given point from a given line. This 

 lem is easily solved for any particular case thus : find 

 equation of the line which passes through the i: 

 hit and which is parallel to the given line lien 



tin- list.mr- (ft) f: origin t<> e.irh of these two 



>S, (3) ami (1)]. and finally Mil. tract one of these 

 mces from the other : the result is the distance between 

 ^iven line and the given point. 



