The equation of the line perpendicular to $2x - 3y + 5 = 0$ and making an intercept of $3$ with the positive $Y$-axis is

If $u = a_1x + b_1y + c_1 = 0$,$v = a_2x + b_2y + c_2 = 0$ and $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$,then the curve $u + kv = 0$ is

If two vertical poles of heights $20\,m$ and $80\,m$ stand apart on a horizontal plane,then the height (in $m$) of the point of intersection of the lines joining the top of each pole to the foot of the other is:

The equation of the line which cuts off the intercepts $2a \sec \theta$ and $2a \csc \theta$ on the axes is

$A$ straight line through the point $P(1, 2)$ makes an angle $\theta$ with the positive $X$-axis in the anticlockwise direction and meets the line $x + \sqrt{3}y - 2\sqrt{3} = 0$ at $Q$. If $PQ = \frac{1}{2}$,then $\theta =$

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