If the line passing through $(4, 3)$ and $(2, k)$ is perpendicular to the line $y = 2x + 3$,then the value of $k$ is:

The angles made with the $X$-axis by the two lines passing through the point $P(1, 2)$ and cutting the line $x+y=4$ at a distance $\frac{\sqrt{6}}{3}$ units from the point $P$ are

The combined equation of the straight lines passing through the point $(4,3)$ and each line making intercepts on the coordinate axes whose sum is $-1$,is

The equation of the line passing through $(4, -6)$ and making an angle of $45^\circ$ with the positive $x$-axis is:

The equation of a line,whose perpendicular distance from the origin is $5$ units and the angle,which the perpendicular to the line from the origin makes,is $210^{\circ}$ with the positive $X$-axis,is

$A$ line $L$ is perpendicular to the line $5x - y = 1$ and the area of the triangle formed by the line $L$ and the coordinate axes is $5$. The equation of the line $L$ is