The equation of the line which passes through the point $(-4, 3)$ and whose portion intercepted between the axes is divided internally in the ratio $5 : 3$ by this point is:

If the normal form of the equation of a straight line $4x + 3y + 2 = 0$ is $x \cos \alpha + y \sin \alpha = p$ and its intercept form is $\frac{x}{a} + \frac{y}{b} = 1$,then $\frac{p \sec \alpha}{ab} = $

The $y$-intercept made by the line $x \cos \alpha + y \sin \alpha = a$ is:

$A$ 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.

Find the equation of the line which intersects the $y$-axis at a distance of $2$ units above the origin and makes an angle of $30^{\circ}$ with the positive direction of the $x$-axis.

Find the equation of the line which passes through $(0, 0)$ with slope $m$.