Coordinate geometry - bisector of two lines

  1. Two lines - a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are given
    I know that the equation of its bisectors is
    a1x + b1y + c1 / √a1^2 + b1^2 = +- a2x + b2y + c2 / √a2^2 + b2^2

    But i intend to find which one is the obtuse angle bisector and which one is the acute angle bisector. I want to find a general formula
    Assuming c1 , c2 both are of same sign
    My text says if a1a2 + b1b2 > 0 and if we take the positve sign we get the obtuse angle bisector - and after many examples i think its true

    But i want to prove it using general equation of line
    I tried to find the angle between bisector adn original line
    i.e. tan θ = m1 - m2 / 1+ m1m2 and then if it is greater than one it will be of obtuse angle but calculations are tough if we use general equation of line

    Any simple proof of the following statement:
    Assuming c1 , c2 both are of same sign
    IF a1a2 + b1b2 > 0 then if we take positve sing we get the obtuse angle bisector

    Thank you!
     
  2. jcsd
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