If two equal sides of an isosceles triangle are given by the equations $7x-y+3=0$ and $x+y-3=0$,then the equation of its third side passing through the point $(2,-5)$ is

Let $A, B, C$ be three points in the $xy$-plane,whose position vectors are given by $\sqrt{3} \hat{i} + \hat{j}$,$\hat{i} + \sqrt{3} \hat{j}$,and $a \hat{i} + (1 - a) \hat{j}$ respectively with respect to the origin $O$. If the distance of the point $C$ from the line bisecting the angle between the vectors $\overrightarrow{OA}$ and $\overrightarrow{OB}$ is $\frac{9}{\sqrt{2}}$,then the sum of all the possible values of $a$ is :

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

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

The equation of the perpendicular bisector of the line segment joining the points $(1, 2)$ and $(-2, 0)$ is:

If the line $l_1: 3y - 2x = 3$ is the angular bisector of the lines $l_2: x - y + 1 = 0$ and $l_3: \alpha x + \beta y + 17 = 0$,then $\alpha^2 + \beta^2 - \alpha - \beta$ is equal to