Find the slope of the line,which makes an angle of $30^{\circ}$ with the positive direction of the $y$-axis measured anticlockwise.

Given that lines $L_1: y=m_a x, L_2: y=m_b x$ and $L_3: y=m_c x$ make equal intercepts on the line $x+y=1$,then

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

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

If a straight line is at a distance of $10$ units from the origin and the perpendicular drawn from the origin to it makes an angle of $\frac{\pi}{4}$ with the negative $X$-axis in the negative direction,then the equation of that line is:

Three points $P(h, k)$,$Q(x_{1}, y_{1})$ and $R(x_{2}, y_{2})$ lie on a line. Show that $(h-x_{1})(y_{2}-y_{1}) = (k-y_{1})(x_{2}-x_{1})$.