Question

The equation of the bisector of obtuse angle formed by the lines 3x+4y-11=0 and 12x-5y-2=0 will be .

• A. 11x-3y-17=0
• B. 11x+3y-17=0
• C. 3x+11y-19=0
• D. 3x-11y+19=0

Answer 1

The correct option is D 3x-11y+19=0

Constant terms of both the equations are of same sign.
Comparing the first and second equation with
$a_{1}x+b_{1}y+c_1=0and{a}_{2}x+b_{2}y+c_2=0respectively,weget$$a_1{a}_2+b_1{b}_2=36-20=16=+ve$
$\therefore$ +ve sign will give the equation of the obtuse angle bisector.
$\Rightarrow \frac{3x+4y-11}{\sqrt{3^2}+\sqrt{4^2}}=\frac{12x-5y-2}{\sqrt{{12}^2}+\sqrt{(-5{)}^2}}\Rightarrow \frac{3x+4y-11}{5}=\frac{12x-5y-2}{13}\Rightarrow 39x+52y-143=60x-25y-10\Rightarrow 21x-77y+133=0\Rightarrow 3x-11y+19=0$