The value of $k (> 0)$,such that the angle between the lines $4x - y + 7 = 0$ and $kx - 5y - 9 = 0$ is $45^{\circ}$,is

The angle between the lines $2x + 11y - 7 = 0$ and $x + 3y + 5 = 0$ is

Show that the equation of the line passing through the origin and making an angle $\theta$ with the line $y=mx+c$ is $\frac{y}{x}=\frac{m \pm \tan \theta}{1 \mp m \tan \theta}$.

If $S_1$ and $S_2$ are two straight lines such that the reflection of $S_1$ in $S_2$ and the reflection of $S_2$ in $S_1$ coincide,the angle between $S_1$ and $S_2$ is equal to?

The acute angle between the lines $x \sin \theta - y \cos \theta = 5$ and $x \sin \alpha - y \cos \alpha + 11 = 0$ is

The equations of the lines passing through $(1,1)$ and making an angle of $45^{\circ}$ with the line $x+y=0$ are