What is the nature of the points $(-a, -b)$,$(0, 0)$,$(a, b)$,and $(a^2, ab)$?

For $a, b, c \in R$,if $6 a^2-3 b^2-c^2+7 a b-a c+4 b c=0$ and $|a|+|b| \neq 0$,then all the lines given by $a x+b y+c=0$ are

The point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ lies on the line

The equation of a line passing through the point of intersection of the lines $x - 2y + 8 = 0$ and $3x - y + 4 = 0$ and passing through the origin is

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

The number of integral values of $\alpha$ for which the abscissa of the point of intersection of the lines $y = x + 9\alpha$ and $3\alpha x + 2y + 9 = 0$ is an integer,is