The straight lines $x+3y-9=0$,$4x+5y-1=0$,and $px+qy+10=0$ are concurrent. If the line $5x+6y+10=0$ passes through the point $(a, b)$,find the point.

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

The lines $2x + y - 1 = 0$,$ax + 3y - 3 = 0$,and $3x + 2y - 2 = 0$ are concurrent for

If $x+2y-3=0$,$3x+4y-7=0$,$2x+3y-4=0$,and $4x+5y-6=0$ are the equations of four lines,then

If $\begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix} = 0$, then the lines $a_i x + b_i y + c_i = 0$ $(i = 1, 2, 3)$ represent:

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 :-