The bisector of the acute angle formed between the lines $4x - 3y + 7 = 0$ and $3x - 4y + 14 = 0$ has the equation

The equation of bisectors of the angles between the lines $|x| = |y|$ 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:

If the lengths of the perpendiculars drawn from a point $(a, b)$ to the lines $2x + 3y + 4 = 0$ and $3x - 2y + 4 = 0$ are equal,then the point $(a, b)$ lies on the line

Let $A(1,0)$, $B(2,-1)$, and $C(\frac{7}{3},\frac{4}{3})$ be three points. If the equation of the internal angle bisector of $\angle ABC$ is $\alpha x+\beta y=5$, then the value of $\alpha^2+\beta^2$ 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.