A line $L$ perpendicular to the line $5 x-12 y+6=0$ makes positive intercept on the $Y$-axis. If the distance from the origin to the line $L$ is 2 units and the angle made by the perpendicular drawn from the origin to the line $L$ with positive $X$-axis is $\theta$, then $\tan \theta+\cot \theta=$

If a line $L$ passing through a point $A(2,3)$ intersects another line $4 x-3 y-19=0$ at the point $B$ such that $A B=4$, then the angle made by the line $L$ with positive $X$-axis in anti-clockwise direction is

A variable straight-line $L$ with negative slope passes through the point $(4,9)$ and cuts the positive coordinate axes in $A$ and $B$. If $O$ is the origin, then the minimum value of $O A+O B$ is

If $4 x^2+12 x y+9 y^2+2 g x+2 f y-1=0$ represent a pair of parallel lines, then