Question

Consider two lines, $L_1:2x+y+4=0$ and $L_2:2x+4y+5=0$, then

• A. Bisector of angle containing origin is $2x-2y+3=0.$
• B. Bisector of acute angle is $6x+6y+13=0$.
• C. Angle containing origin is acute angle.
• D. Angle containing origin is obtuse.

Answer 1

Answer: (A), (B), (D)

$C_1,C_2$ are both positive
(1) Bisector of angle containing origin
$\frac{2x+y+4}{\sqrt{5}}=\frac{2x+4y+5}{2\sqrt{5}}$
$4x+2y+8=2x+4y+5$
$2x-2y+3=0$
(2) Since $a_1{a}_2+b_1{b}_2>0\Rightarrow$ origin occurs in obtuse angle. bisector of acute angle
$\frac{2x+y+4}{\sqrt{5}}=\frac{-(2x+4y+5)}{2\sqrt{5}}$
$2x+y+4=-2x-4x-5$
$4x+5y+8=-2x-4-5$
$6x+6y+13=0$