If the three distinct lines $x + 2ay + a = 0$,$x + 3by + b = 0$,and $x + 4ay + a = 0$ are concurrent,then the point $(a, b)$ lies on a

The three straight lines $ax + by = c$,$bx + cy = a$ and $cx + ay = b$ are concurrent,if

The equation of the line passing through the point of intersection of the lines $x-3y+2=0$ and $2x+5y-7=0$ and perpendicular to the line $3x+2y+5=0$ is:

Let $C$ be the centroid of the triangle with vertices $(3, -1), (1, 3),$ and $(2, 4).$ Let $P$ be the point of intersection of the lines $x + 3y - 1 = 0$ and $3x - y + 1 = 0.$ Then the line passing through the points $C$ and $P$ also passes through the point

Which of the following lines is concurrent with the lines $3x + 4y + 6 = 0$ and $6x + 5y + 9 = 0$?

If the points $(x + 1, 2)$,$(1, x + 2)$,and $\left( \frac{1}{x + 1}, \frac{2}{x + 1} \right)$ are collinear,then $x$ is