Question

The equation of the bisector of the angle between the lines $x-7y+5=0,5x+5y-3=0$ which is the supplement of the angle containing the origin will be

• A. $x+3y-2=0$
• B. $x-3y+2=0$
• C. $3x-y+1=0$
• D. $x+y+2=0$

Answer 1

The correct option is A $x+3y-2=0$

$x-7y+5=0$, $c_1=+5$ +ve and $5x+5y-3=0$, $c_2=-3$ -ve

Equation angle bisector containing origin is given by

$-\frac{(x-7y+5)}{\sqrt{50}}=+\frac{(5x+5y-3)}{\sqrt{50}}$

$\therefore 6x-2y-8=0$

$\Rightarrow 3x-y-4=0$

But we have to find angle bisector which is the supplement of the angle containing the origin

So, $+(x-7y+5)=+(5x+5y-3)$

$\Rightarrow 4x+12y-8=0$

$\Rightarrow x+3y-2=0$