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

The angle between the lines $x \cos 30^\circ + y \sin 30^\circ = 3$ and $x \cos 60^\circ + y \sin 60^\circ = 5$ is .....$^\circ$

The equation of a straight line passing through the point $(1, 2)$ and inclined at $45^{\circ}$ to the line $y = 2x + 1$ is

The angle between the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{a} - \frac{y}{b} = 1$ is

If a straight line $L$ passing through the point $(5, -3)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3}x + y - 9 = 0$ and $L$ intersects the $X$-axis,then the equation of $L$ 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