6.Perpendicular distance from outside point P(x1,y1) ( not lying on a line) on a line x cos a + y sin a = p
is
| x₁ cos a + y₁ sin a – p | .
7.To find the point of intersection of two lines—
Lines must be non-parallel line . Its mean parallel line does not meet .
Suppose , the two lines be
a₁x + b₁y + c₁ = 0. and a₂x + b₂y + c₂ = 0
If (x₁ , y₁ ) be the co-ordinates of their point of intersection—
Then
a₁x + b₁y + c₁ = 0. and
a₂x + b₂y + c₂ = 0
solving these two equation and find ( x , y )
8.Concurrent lines :
If three given lines are concurrent they must be meet in a common point.
Method to find concurrency—
Method 1.
Firstly we find point of intersection on solving any two lines. If this point satisfy the third equation also , the given lines are concurrent.
Method 2.
Determinant form
Let three lines a ᵢ x + b ᵢ y + c ᵢ = 0
i = 1 ,2 ,3 are concurrent if