Question

The equations of the bisectors of that angle between the lines $x+2y-11=0,3x+6y-5=0$ which contains the point $(1,-3)$ is

• A. $3x=19$
• B. $3y=7$
• C. $3x=19$ and $3y=7$
• D. None of these

Answer 1

The correct option is A $3x=19$

$$\begin{array}{cccc}\text{Solution}-& x+2y=11-& 3x-6y=5-\left(2\right)& \\ & \frac{x}{11}+\frac{2y}{\frac{11}{2}}=1& \frac{x}{5/3}+\frac{y}{-5/6}& =1\\ m& =\frac{-1}{2}& & m=\frac{1}{2}\end{array}$$Solving (1) and (2) we get $x=\frac{71}{6}=\frac{19}{3}\text{and}y=\frac{7}{3}$

Therefore, the equation of bisector comes out to be $3x=19$

Hence, (A) is the correct option