Question

Consider two lines $L_1=2x-y+4=0$ and $L_2=x-2y-1=0$, then which of the following is/are correct.

• A. acute angle bisector of $L_1$ and $L_2$ is $x-y+4=0$
• B. obtuse angle bisector of $L_1$ and $L_2$ is $x+y+5=0$
• C. acute angle of the lines contains the origin
• D. acute angle between $L_1$ and $L_2$ is ${\tan }^{-1}\left(\frac{7}{4}\right)$

Answer 1

Answer: (B)

obtuse angle bisector of $L_1$ and $L_2$ is $x+y+5=0$

The Equation for finding angle bisector is $\left|\frac{a_{1}x+b_{1}y+c_1}{\sqrt{a_1^2+b_1^2}}\right|=\left|\frac{a_{2}x+b_{2}y+c_2}{\sqrt{a_2^2+b_2^2}}\right|$

Therefore,

$\left|\frac{2x-y+4}{\sqrt{2^2+1^2}}\right|=\left|\frac{x-2y-1}{\sqrt{1^2+2^2}}\right|$

On solving, we get two lines:

acute angle bisector and obtuse angle bisector $x+y+5=0x-y+1=0$

By plotting the lines, we get that the obtuse angle bisector is $x+y+5=0$