What are the equations of the two lines passing through the point $(7, 9)$ and making an angle of $60^{\circ}$ with the line $x - \sqrt{3}y - 2\sqrt{3} = 0$?

The line passing through the points $(3, -4)$ and $(-2, 6)$ and the line passing through $(-3, 6)$ and $(9, -18)$ are:

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

Two lines pass through the point $(2,3)$ and intersect each other at an angle of $60^{\circ}$. If the slope of one line is $2$,find the equations of the other line.

If the two lines $\frac{3}{2} x + (2a - 1)y = 3$ and $2x + a^2y = -3$ are perpendicular,then the distance of their point of intersection from the point $(1, 1)$ is

Let $\theta_1$ be the angle between two lines $2x + 3y + c_1 = 0$ and $-x + 5y + c_2 = 0$,and $\theta_2$ be the angle between two lines $2x + 3y + c_1 = 0$ and $-x + 5y + c_3 = 0$,where $c_1, c_2, c_3$ are any real numbers.
Statement-$1$: If $c_2$ and $c_3$ are proportional,then $\theta_1 = \theta_2$.
Statement-$2$: $\theta_1 = \theta_2$ for all $c_2$ and $c_3$.