The points $A(1, 2)$,$B(2, 4)$,and $C(4, 8)$ form a/an

If the lines $2x + y - 3 = 0$,$3x + 2y - 2 = 0$,and $kx - 3y - 23 = 0$ are concurrent,then the roots of the equation $6x^2 - 7x + k = 0$ are

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 $.........$

If the lines $x+y-1=0$,$kx+2y+1=0$,and $4x+2ky+7=0$ are concurrent,then $k=$

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 $d^2 = \dots$

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