The acute angle between the lines $y = 3$ and $y = \sqrt{3}x + 9$ is .....$^o$

If $m_1$ and $m_2$ $(m_1 > m_2)$ are the slopes of the lines which make an angle of $30^{\circ}$ with the line joining the points $(1, 2)$ and $(3, 4)$,then $\frac{m_1}{m_2} = $

If $\frac{1}{ab'} + \frac{1}{ba'} = 0,$ then the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b'} + \frac{y}{a'} = 1$ are

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 equations of the lines passing through the point $(3,2)$ which make an angle of $45^{\circ}$ with the line $x-2y=3$ are

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