If a line $ax + 2y = k$ forms a triangle of area $3$ sq. units with the coordinate axes and is perpendicular to the line $2x - 3y + 7 = 0$,then the product of all the possible values of $k$ is

If the equation of the base of an equilateral triangle is $2x - y = 1$ and the vertex is $(-1, 2)$,then the length of the side of the triangle is

Among the statements:
$(S1)$ : If $A(5, -1)$ and $B(-2, 3)$ are two vertices of a triangle, whose orthocentre is $(0, 0)$, then its third vertex is $(-4, -7)$ and
$(S2)$ : If positive numbers $2a, b, c$ are three consecutive terms of an $A.P.$, then the lines $ax + by + c = 0$ are concurrent at $(2, -2)$.

Three lines $x + 2y + 3 = 0$,$x + 2y - 7 = 0$,and $2x - y - 4 = 0$ form three sides of two squares. Find the equation of the fourth side of each square.

$L_1 \equiv 2x+y-3=0$ and $L_2 \equiv ax+by+c=0$ are two equal sides of an isosceles triangle. If $L_3 \equiv x+2y+1=0$ is the third side of this triangle and $(5,1)$ is a point on $L_2=0$,then $\frac{b^2}{|ac|}=$

$A$ line is such that its segment between the lines $5x - y + 4 = 0$ and $3x + 4y - 4 = 0$ is bisected at the point $(1, 5)$. Obtain its equation.