The equation of a straight line passing through $(3, 2)$ and cutting an intercept of $2 \text{ units}$ between the lines $3x + 4y = 11$ and $3x + 4y = 1$ is:

The number of points having a distance of $\sqrt{5}$ from the straight line $x-2y+1=0$ and a distance of $\sqrt{13}$ from the line $2x+3y-1=0$ is:

If a straight line $L$ perpendicular to the line $3x - 4y = 6$ forms a triangle of area $6$ square units with the coordinate axes,then the minimum perpendicular distance from the point $(1, 1)$ to the line $L$ is

The number of integer values of $m$,for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer,is

The number of integral values of $m$,for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is an integer,is:

The origin and the points where the line $L_1$ intersects the $x$-axis and $y$-axis are vertices of a right-angled triangle $T$ whose area is $8$. Also,the line $L_1$ is perpendicular to the line $L_2: 4x - y = 3$. Then,the perimeter of triangle $T$ is: