$a$ and $b$ are the intercepts made by a line on the coordinate axes. If $3a = b$ and the line passes through $(1, 3)$,then the equation of the line is

Find the equation of the line passing through the point $(4, 3)$ such that the sum of its intercepts on the axes is $-1$.

If the coordinates of the points $A$ and $B$ are $(1, 0)$ and $(2, \sqrt{3})$,then the angle made by the line $AB$ with the $x$-axis is .....$^o$.

$A$ line passing through the point $P(a, 0)$ makes an acute angle $\alpha$ with the positive $x$-axis. Let this line be rotated about the point $P$ through an angle $\frac{\alpha}{2}$ in the clockwise direction. If in the new position,the slope of the line is $2-\sqrt{3}$ and its distance from the origin is $\frac{1}{\sqrt{2}}$,then the value of $3a^2 \tan^2 \alpha - 2\sqrt{3}$ is

The equation of the line passing through $(1, 2)$ and perpendicular to $3x + 4y + 5 = 0$ is

The equation of a straight line passing through $(-3, 2)$ and cutting an intercept equal in magnitude but opposite in sign from the axes is given by: