Let the line $L_1$ be a line passing through the point $(\mathbf{0},-\mathbf{6})$ and making an angle of $\mathbf{1 5 0}^{\circ}$ with the positive $x$-axis. Then the equation of a line $L_2$ parallel to $L_1$ and crossing the $y$-axis 2 units below the origin is:

A line L passes through the point of intersection of the lines $3 x+y-10=0$ and $x-y-2=0$.

If the perpendicular distance of the line $L$ from the point $(5,1)$ is exactly $\frac{2}{\sqrt{5}}$ units, which of the following represents the correct equation for line L ?

A straight line passes through the point $P\left(\log _2 16, \log _3 27\right)$ such that the portion of the line intercepted between the co-ordinate axes is divided by $P$ in the ratio $1: 2$ internally (starting from the $x$-axis). Then the equation of the line is:

Distance between $8 x+15 y-20=0$ and $8 x+15 y+14=0$ is: