If the slope of the line $ax + (3 - a)y + 7 = 0$ is $7$,then the value of the integral part of '$a$' is

If the point $(3, -4)$ divides the segment of the line between the $X$-axis and $Y$-axis in the ratio $2 : 3$,then the equation of the line is:

The line joining the points $(-1, 3)$ and $(4, -2)$ will pass through the point $(p, q)$ if

$A$ 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 coordinates of the points $A$ and $B$ are $(3, 3)$ and $(7, 6)$,then the length of the portion of the line $AB$ intercepted between the axes is

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