Question

The equation of the bisector of the angle between two lines 3x – 4y + 12 = 0 and 12x – 5y + 7 = 0, which contain the point (– 1, 4) is

(a) 21x + 27y – 121 = 0

(b) 21x – 27y + 121 = 0

(c) 21x + 27y + 191 = 0

(d) [(– 3x + 4y – 12)/5] = [(12x – 5y + 7)/13]

Answer 1

The correct option (a) 21x + 27y – 121 = 0

Explanation:

Equation of bisector of angle between two line containing point (α, β) is

[(a₁x + b₁y + c)/√(a₁² + b₁²)] = ± [(a₂x + b₂y + c₂)/√(a₂² + b₂²)]

∴ equation of bisector is [(3x – 4y + 12)/5] = ± [(12x – 5y + 7)/13] at point (– 1, 4) value of [(3x – 4y + 12) / (12x – 5y + 7)] > 0 

 ⇒ Take positive sign.

∴ equation is [(3x – 4y + 12)/5] = [(12x – 5y + 7)/13]

∴ 39x – 52y + 156 = 60x – 25y + 35

∴ 21x + 27y – 121 = 0