The least positive value of $t$, so that the lines $x=t+\alpha, y+16=0$ and $y=\alpha x$ are concurrent, is

The equation of the line passing through the point of intersection of the lines $x + 2y + 6 = 0$ and $2x - y = 2$ and making an intercept $5$ on the $y$-axis is

The equation of the line passing through the intersection of the lines $x - y = 4$ and $3x + y = 7$ and parallel to the line $x + 2y = 1$ is:

If lines represented by $x+3y-6=0$,$2x+y-4=0$ and $kx-3y+1=0$ are concurrent,then the value of $k$ is

If the lines $ax + y + 1 = 0, x + by + 1 = 0$ and $x + y + c = 0$ ($a, b, c$ being distinct and different from $1$) are concurrent,then $\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} = $

$(a, b)$ 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