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:

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

Among the statements:
$(S1)$ : If $A(5, -1)$ and $B(-2, 3)$ are two vertices of a triangle,whose orthocentre is $(0, 0)$,then its third vertex is $(-4, -7)$ and
$(S2)$ : If positive numbers $2a, b, c$ are three consecutive terms of an $A.P.$,then the lines $ax + by + c = 0$ are concurrent at $(2, -2)$.

Let a variable line of slope $m > 0$ passing through the point $(4, -9)$ intersect the coordinate axes at the points $A$ and $B$. The minimum value of the sum of the distances of $A$ and $B$ from the origin is

If $l, m, n$ are in arithmetic progression,then the straight line $lx + my + n = 0$ will always pass through the point:

The least distance from the origin to a point on the line $y=x+3$ which lies at a distance of $2$ units from $(0,3)$ is