The lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ are perpendicular to each other,if

If the lines $y = (2 + \sqrt{3})x + 4$ and $y = kx + 6$ are inclined at an angle of $60^{\circ}$ to each other,then the value of $k$ will be

The slopes of the lines,making an angle of $45^{\circ}$ with the line $2x - 3y = 5$,are

Find the acute angle between the lines $y = 3$ and $y = \sqrt{3}x + 9$. (in $^{\circ}$)

The obtuse angle between the lines $y = -2$ and $y = x + 2$ is .....$^o$

$A$ line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $L_1: 2x + y + 6 = 0$ and $L_2: 4x + 2y - p = 0, p > 0$,at the points $A$ and $B$,respectively. If $AB = \frac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point $A$ on the line $L_2$ is $M$,then $\frac{AM}{BM}$ is equal to