Equation of the line passing through the intersection of two lines

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

Let the lines be

Let P (h,k) be the point of intersection of L₁ = 0 and L₂ = 0.

Now consider the following equations,

… (v)

… (vi)

This equation is a first degree in x and y and hence this represents a straight line.

Again, from (iii) and (iv), the coordinates (h,k) satisfy (vi) for all the real values of l.

(vi) represents lines through the point of intersection of lines L₁ = 0 and L₂ = 0.

Hence the set of lines passing through the intersection of lines

Remarks:

The equation of a line contains two arbitrary constants. This means two geometrical conditions must be given to obtain the equation of a line. If a line passes through the intersection of two lines (given) only one geometrical condition is available.

\ L₁ + lL₂ = 0 contains one arbitrary constant  l . A second condition provided has to be used to determine the value of l .