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

If the lines $x+y-2=0$,$3x-4y+1=0$ and $5x+ky-7=0$ are concurrent at $(\alpha, \beta)$,then the equation of the line concurrent with the given lines and perpendicular to $kx+y-k=0$ is

The equation of the line parallel to the $y$-axis and passing through the point of intersection of the lines $ax + by + c = 0$ and $a'x + b'y + c' = 0$ is:

The equations $(b - c)x + (c - a)y + (a - b) = 0$ and $(b^3 - c^3)x + (c^3 - a^3)y + (a^3 - b^3) = 0$ will represent the same line,if

The point of intersection of the lines $(a^3 + 3)x + ay + a - 3 = 0$ and $(a^5 + 2)x + (a + 2)y + 2a + 3 = 0$ (where $a$ is a real number) lies on the $y$-axis for:

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