The joint equation of two lines through the origin, each making an angle with measure of $30^{\circ}$ with the positive Y -axis, is

If the slope of one of the lines given by $\mathrm{K} x^2+6 x y+y^2=0$ is three times the order, then the value of $K$ is

Let $\mathrm{P} \equiv(-5,0), \mathrm{Q} \equiv(0,0)$ and $\mathrm{R} \equiv(2,2 \sqrt{3})$ be three points. Then the equation of the bisector of the angle $P Q R$ is

If the length of the perpendicular to a line from the origin is $2 \sqrt{2}$ units, which makes an angle of $135^{\circ}$ with the X -axis, then the equation of line is