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

Lines $L_1: y-x=0$ and $L_2: 2x+y=0$ intersect the line $L_3: y+2=0$ at $P$ and $Q$,respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersects $L_3$ at $R$.
$STATEMENT-1$ : The ratio $PR:RQ$ equals $2\sqrt{2}:\sqrt{5}$.
$STATEMENT-2$ : In any triangle,the angle bisector divides the opposite side in the ratio of the sides containing the angle.

Let $u \equiv ax + by + a \sqrt[3]{b} = 0$ and $v \equiv bx - ay + b \sqrt[3]{a} = 0$ where $a, b \in R$ be two straight lines. The equation of the bisectors of the angle formed by $k_1u - k_2v = 0$ and $k_1u + k_2v = 0$ for non-zero real $k_1$ and $k_2$ are:

Let the line $L_1 : x + 3 = 0$ intersect the lines $L_2 : x - y = 0$ and $L_3 : 3x + y = 0$ at the points $A$ and $B$,respectively. Let the bisector of the obtuse angle between the lines $L_2$ and $L_3$ intersect the line $L_1$ at the point $C$. Then $BC^2 : AC^2$ is equal to:

Let three points be $P(-1, 0)$,$Q(0, 0)$,and $R(3, 3\sqrt{3})$. The equation of the angle bisector of $\angle PQR$ is:

The equation of the bisector of the acute angle between the lines $2x - y + 4 = 0$ and $x - 2y - 1 = 0$ is