Question

For the straight lines 4x + 3y – 6 = 0 and 5x + 12y + 9 = 0, the equation of the bisector of the obtuse angle between them is

• A. 9x – 7y – 41 = 0
• B. 7x + 9y – 3 = 0
• C. 7x + 9y – 3 = 0
• D. None of these

Answer 1

The correct option is A

9x – 7y – 41 = 0

The given lines are

4x + 3y – 6 = 0 or –4x – 3y + 6 = 0 …… (1)

and 5x + 12y + 9 = 0 …… (2)

$Here{a}_1=-4,a_2=5,b_1=-3,b_2=12$

$Now,a_1{a}_2+b_1{b}_2=-20-36=-56$<0

$\therefore$ The equation of the bisector of the obtuse angle between the lines (1) and (2) is

$\frac{-4x-3y+6}{\sqrt{(-4{)}^2+(-3{)}^2}}=-\frac{5x+12y+9}{\sqrt{5^2+(12{)}^2}}$

$\Rightarrow$ 13(–4x – 3y + 6) = –5(5x + 12y + 9)

$\Rightarrow$ 27x – 21y – 123 = 0 or 9x – 7y – 41 = 0