The minimum area of the triangle formed by the variable line $3 \cos \theta \cdot x + 4 \sin \theta \cdot y = 12$ and the coordinate axes is

$A$ line $L$ perpendicular to the line $5x - 12y + 6 = 0$ makes a 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 the positive $X$-axis is $\theta$,then $\tan \theta + \cot \theta =$

If the midpoints of the sides $BC, CA$ and $AB$ of the triangle $ABC$ are $(1, 3), (5, 7)$ and $(-5, 7)$ respectively,then the equation of the side $AB$ is

If $(a, 8)$ is a point on the line segment joining $(2, 5)$ and $(4, -1)$,then the value of $a$ is:

The slope of a line passing through $P(2, 3)$ and intersecting the line $x + y = 7$ at a distance of $4$ units from $P$ is

$A$ line meets the $x$-axis and $y$-axis at the points $A$ and $B$ respectively. If the midpoint of $AB$ is $(x_1, y_1)$,then the equation of the line is: