The locus of the points which are at an equal distance from $3x + 4y - 11 = 0$ and $12x + 5y + 2 = 0$ and which is near the origin is:

The 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 angle between $L_1$ and $L_2$ divides the line segment $PQ$ internally at $R$.
Statement-$I$: $PR:RQ = 2\sqrt{2}:\sqrt{5}$
Statement-$II$: In any triangle,the bisector of an angle divides the opposite side in the ratio of the sides containing the angle.

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

Let distinct lines $L_1$ and $L_2$ belong to the family of lines $(x - 2y - 3) + \lambda (x + 3y + 2) = 0$. If $B_1$ is the angle bisector of $L_1$ and $L_2$ which passes through the point $A(2, 3)$,then the equation of the other bisector of $L_1$ and $L_2$ is ($\lambda$ is a parameter).

The equation of the line which bisects the obtuse angle between the lines $x - 2y + 4 = 0$ and $4x - 3y + 2 = 0$ is:

The equations of two equal sides of an isosceles triangle are $7x - y + 3 = 0$ and $x + y - 3 = 0$. If the third side passes through the point $(1, -10)$,find the equation of the third side.