Question

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

• A. $3x=17$
• B. $3x=19$
• C. $3x=19$ & $3y=7$
• D. None of these

Answer 1

Answer: (B)

$3x=19$

The point $(1,-3)$ when substituted in the given equations of lines gives opposite sign i.e.$-16,16$.
Hence the bisector of angle in which $(1,-3)$ lies is obtained by taking '$-$' out of $\pm$ sign
$\therefore \frac{x+2y-11}{\sqrt{5}}=-\frac{3x-6y-5}{3\sqrt{5}}$
$\Rightarrow 3(x+2y-11)=-(3x-6y-5)$
$\Rightarrow 3x=19$
$\Rightarrow$ Hence choice (b) is correct answer