The equation of the line perpendicular to $x = c$ is

Find the equation of the line which passes through $(2, 2\sqrt{3})$ and is inclined with the $x-$axis at an angle of $75^{\circ}$.

If a line $L$ passing through a point $A(2, 3)$ intersects another line $4x - 3y - 19 = 0$ at the point $B$ such that $AB = 4$,then the angle made by the line $L$ with the positive $X$-axis in the anti-clockwise direction is

Find the equations of the sides $QR$ and $RP$ of a triangle $PQR$ where $P = (2, 1)$,and the sides $QR$ and $RP$ have slopes $m_1 = \frac{2}{\sqrt{3}}$ and $m_2 = -\frac{2}{\sqrt{3}}$ respectively,passing through the origin $(0, 0)$ for $QR$ and intersecting at $P(2, 1)$ for $RP$.

The area of the triangle formed by the line $L$ with the coordinate axes is $12$ sq. units. If $L$ passes through the point $(12, 4)$ and the product $P$ of the $X$-intercept of $L$ and the square of the $Y$-intercept of $L$ is negative,then $P=$

The equation of a line passing through the point $(1, 2)$ whose distance from the point $(3, 1)$ is the greatest is