If the lines $x+2ay+a=0$,$x+3by+b=0$,and $x+4cy+c=0$ are concurrent,then $a, b, c$ are in

If the lines $3x + 4y - 5 = 0$,$2x + 3y - 4 = 0$,and $px + 4y - 6 = 0$ all meet at the same point,then $p$ is equal to:

$(a, b)$ is the point of concurrency of the lines $x-3y+3=0$,$kx+y+k=0$,and $2x+y-8=0$. If the perpendicular distance from the origin to the line $L \equiv ax-by+2k=0$ is $p$,then the perpendicular distance from the point $(2, 3)$ to $L=0$ is

If the three lines $p_1x + q_1y = 1$,$p_2x + q_2y = 1$,and $p_3x + q_3y = 1$ are concurrent,then the points $(p_1, q_1)$,$(p_2, q_2)$,and $(p_3, q_3)$ are:

The line passing through the intersection of the lines $ax + 2by + 3b = 0$ and $bx - 2ay - 3a = 0$ (where $(a, b) \neq (0, 0)$) and parallel to the $x$-axis is:

The line $(2 + k)x + (1 + k)y = 5 + 7k$ passes through a fixed point for all values of $k$. If $d$ is the distance of this fixed point from the origin, then $d^2 = \dots$