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

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

If the lines $2x + y - 3 = 0$,$3x + 2y - 2 = 0$,and $kx - 3y - 23 = 0$ are concurrent,then the roots of the equation $6x^2 - 7x + k = 0$ are

If $k_{i}$ are possible values of $k$ for which lines $kx + 2y + 2 = 0$,$2x + ky + 3 = 0$,and $3x + 3y + k = 0$ are concurrent,then $\sum k_{i}$ has the value

For what values of $\theta$ are the points $(1, 1), (0, \sec^{2}\theta), (\csc^{2}\theta, 0)$ collinear?

If the lines $4x + 3y - k = 0$,$2x + y + 3 = 0$,and $3x + 2y + k = 0$ are concurrent,then the perpendicular distance from the point of concurrency of these lines to the line $3x + 4y + 2 = 0$ is