What is the normal form of the line $x + \sqrt{3}y - 4 = 0$?

$A$ straight line passing through the point $(2, 2)$ intersects the lines $\sqrt{3}x + y = 0$ and $\sqrt{3}x - y = 0$ at points $A$ and $B$ respectively. Find the equation of the line $AB$ such that the triangle $OAB$ is an equilateral triangle,where $O$ is the origin.

The equation of the lines on which the perpendiculars from the origin make a $30^\circ$ angle with the $x$-axis and which form a triangle of area $\frac{50}{\sqrt{3}}$ with the axes,are

The equation of the straight line cutting off an intercept of $2$ from the negative direction of the $y$-axis and inclined at $30^\circ$ to the positive direction of the $x$-axis is:

The gradient of the line joining the points on the curve $y = x^2 + 2x$ whose abscissae are $1$ and $3$,is

The number of straight lines which are equally inclined to both the axes is