Equations of the bisectors of angles between the lines ax + by + c = 0 &
a ′ x + b ′ y + c ′ = 0 (ab ′ ≠ a ′ b) are: 
= ± 
If aa ′ + bb ′ < 0, then the equation of the bisector of this acute angle is
= + 
If, however, aa ′ + bb ′ > 0, the equation of the bisector of the obtuse angle is :
= + 
(i) The equation of the bisector of the acute angle between the lines 3x – 4y + 7 = 0 and
12x + 5y – 2 = 0 is
Text Solution
Verified by ExpertsB
(i) after making constant terms positive, equation of lines are
3x – 4y + 7 = 0 ... (i)
– 12x – 5y + 2 = 0 ... (ii)
a 1 a 2 + b 1 b 2 = – 36 + 20 < 0
∴ equation of acute angle bisector is
= + 
⇒ 11x – 3y + 9 = 0
(ii) p = 
= 
q = 
= 
p < q Hence 2x – 16y – 5 = 0 is acute angle bisector
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