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. $3x+y+2=0$

Answer 1

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

Equation of the bisector of line $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ is

$\left|\frac{a_{1}x+b_{1}y+c_1}{\sqrt{a_1^2+b_1^2}}\right|=\left|\frac{a_2+b_{2}y+c_2}{\sqrt{a_2^2+b_2^2}}\right|$

for origin containing bisector.

$\frac{a_{1}x+b_{1}y+c_1}{\sqrt{a_1^2+b_1^2}}z+\frac{a_{2}x+b_{2}y+c_2}{\sqrt{a_2^2+b_2^2}}$

Provide $c_1$ & $c_2$ must of some sign and for non-origin containing

$\frac{a_{1}x+b_{1}y+c_1}{\sqrt{a_1^2+b_1^2}}z=\frac{a_{2}x+b_{2}y+c_2}{\sqrt{a_2^2+b_2^2}}$

[$c_1$ & $c_2$ must be of same sign]

In this question

$\frac{x-4y+2}{\sqrt{1+49}}z-\left[\frac{-5x-5y+3}{\sqrt{25+25}}\right]$

$\Rightarrow x-7y+5z5x+5y-3$

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

$x+3y=2$