Find the direction in which a straight line must be drawn through the point $$(1,2)$$ so that its point of intersection with the line $$x+y=4$$ may be at a distance of $$\sqrt{\frac{2}{3}}$$ from this point.

The perpendicular distance of a line from the origin is 5 units and its slope is $$-1$$. The equation of the line is

Let the equation of pair of lines $$y=m_1 x$$ and $$y=m_2 x$$ can be written as $$\left(y-m_1 x\right)\left(y-m_2 x\right)=0$$. Then, the equation of the pair of the angle bisector of the line $$3 y^2-5 x y-2 x^2=0$$ is

The distance of the point $$(3,4)$$ from the line $$3 x+2 y+7=0$$ measured along the line parallel to $$y-2 x+7=0$$ is equal to