If the lines $L_1 \equiv x-2y+3=0$,$L_2 \equiv 2x+y+1=0$,and $L_3 \equiv 3x+y+c=0$ are concurrent and $\theta$ is the acute angle between the lines $L_1=0$ and $L_3=0$,then $\tan \theta=$

If the sum of squares of all real values of $\alpha$,for which the lines $2x - y + 3 = 0$,$6x + 3y + 1 = 0$,and $\alpha x + 2y - 2 = 0$ do not form a triangle is $p$,then the greatest integer less than or equal to $p$ is $.........$

The line $(2 + k)x + (1 + k)y = 5 + 7k$ passes through a fixed point for all values of $k$. If $d$ is the distance of this fixed point from the origin, then $d^2 = \dots$

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

$(x_1, y_1)$ is the point of concurrency of a family of lines. If the algebraic sum of the lengths of the perpendiculars drawn to these lines from $(2, 0)$,$(0, 2)$,and $(1, 1)$ is zero,then $(x_1, y_1) =$

The equation of the line passing through the point of intersection of lines $2x - y + 2 = 0$ and $x + y + 4 = 0$ and the point $(5, -2)$ is