Equations of bisectors of the angles between the given lines are
4x+3y−6√42+32=±5x+12y+9√52+122
⇒4x+3y−6√16+9=±5x+12y+9√25+144
⇒4x+3y−6√25=±5x+12y+9√169
⇒4x+3y−65=±5x+12y+913
⇒52x+39y−78=±(25x+60y+45)
⇒52x+39y−78=25x+60y+45,52x+39y−78=−25x−60y−45
⇒27x+21y−123=0 and 77x+99y−33=0
⇒9x+7y−41=0 and 7x+9y−3=0
If θ is the acute angle between the line 4x+3y–6=0 and the bisector 9x–7y–41=0, then
tanθ=∣∣
∣
∣
∣∣−43−971+(−43)97∣∣
∣
∣
∣∣=∣∣∣−28−2721−36∣∣∣=5515=113>1
Hence the bisector of the obtuse angle is 9x–7y–41=0