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

The acute angle between the lines given by $y - \sqrt{3}x + 1 = 0$ and $\sqrt{3}y - x + 7 = 0$ is (in $^{\circ}$)

The angle between the line joining the points $(1, -2)$ and $(3, 2)$ and the line $x + 2y - 7 = 0$ is

The equations of the lines passing through the origin and making an angle of $60^{\circ}$ with the line $x + y\sqrt{3} + 3\sqrt{3} = 0$ are

If the lines $y=3x+1$ and $2y=x+3$ are equally inclined to the line $y=mx+4$,find the value of $m$.

$A$ 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