If the lines drawn along the diagonals of the two squares formed by two pairs of lines $x^2-3|x|+2=0$ and $y^2-3y+2=0$ form a square $ABCD$,then the equations of two adjacent sides of the square $ABCD$ are

Let $A(-1, 1)$,$B(3, 4)$,and $C(2, 0)$ be three given points. $A$ line $y = mx$,$m > 0$,intersects lines $AC$ and $BC$ at points $P$ and $Q$ respectively. Let $A_1$ and $A_2$ be the areas of $\Delta ABC$ and $\Delta PQC$ respectively,such that $A_1 = 3A_2$. Then the value of $m$ is equal to:

One vertex of an equilateral triangle is $(2, 3)$ and the line of its opposite side is $x + y = 2$. Find the equations of the other two sides.

If the perpendicular bisector of the line segment joining $A(\alpha, 3)$ and $B(2, -1)$ has $y$-intercept $1$,then $\alpha =$

If $P(x_1, y_1)$ and $Q(x_2, y_2)$ are points on $2x + 3y + 1 = 0$ such that $|PA - PB|$ is maximum and $|QA - QB|$ is minimum,where $A(2, 0)$ and $B(0, 2)$,then the value of $x_1 - y_1 + x_2 - y_2$ is -

If $a, b, c$ are in $A.P.$,then the straight line $ax + by + c = 0$ will always pass through the point