$A$ value of $k$ such that the straight lines $y-3kx+4=0$ and $(2k-1)x-(8k-1)y-6=0$ are perpendicular is

The lines $y = 2x$ and $x = -2y$ are

The angle between the lines $x \cos \alpha_1 + y \sin \alpha_1 = p_1$ and $x \cos \alpha_2 + y \sin \alpha_2 = p_2$ is

The line passing through the points $(3, -4)$ and $(-2, 6)$ and the line passing through $(-3, 6)$ and $(9, -18)$ are:

$A$ straight line $L$ through the point $(3, -2)$ is inclined at an angle of $60^o$ to the line $\sqrt{3}x + y = 1$. If $L$ also intersects the $x$-axis,then the equation of $L$ is

The acute angle between the lines $x-3=0$ and $x+y=19$ is: (in $^{\circ}$)