GEOMETRY 



2.104 The two lines: 



intersect at the point : 



y = aix + bi, 

 y = oix + 2 , 



0i 02 0i 02 



2.105 If < is the angle between the two lines 2.104 : 



, #1 



tan d> = - 



I 



2.106 Equations of two parallel lines : 



Ax + By + Ci = o | y = ax -f #1, 



-4# + By + C 2 = o \ y = ax + b%. 



2.107 Equations of two perpendicular lines : 



Ax + By + Ci = o ( y = ax + b ly 



Bx Ay + Cz = o ] ^ 



2.108 Equation of line through x\ t y\ and parallel to the line : 



Ax + By + C = o or y = ax + 6, 



.4 (a? - Ji) + 5(y - yi) = o or y - yi = a(x - ^i). 



2.109 Equation of line through x i} yi and perpendicular to the line 



Ax + By + C = o or y = a# + 6, 



/Y _ A* 



B(* - ^i) - A (y - yi) = o or y - yi = -- 



2.110 Equation of line through xi, y\ making an angle with the line y ax + b 



a + tan <f> , N 



y - yi= i- tan^ ( ^-^ 



2.111 Equation of line through the two points, x\, yi, and ^2, ^2 : 



2.112 Perpendicular distance from the point xi, yi to the line 

 Ax + By + C = o or y = ax + b, 



yi - axi-b 



or p = 



2.113 Polar equation of the line y = ax -{- b: 



b cos ex 



r = 



sin (19 - a) J 

 where 



tan a = a. 



