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 straight lines $l_1$ and $l_2$ pass through the origin and trisect the line segment of the line $L: 9x + 5y = 45$ between the axes. If $m_1$ and $m_2$ are the slopes of the lines $l_1$ and $l_2$,then the point of intersection of the line $y = (m_1 + m_2)x$ with $L$ lies on

The equation of the line passing through the intersection of $3x - 4y + 1 = 0$ and $5x + y - 1 = 0$ which cuts off equal intercepts on the axes is given by

$A$ is the point of intersection of the lines $3x + y - 4 = 0$ and $x - y = 0$. If a line having a negative slope makes an angle of $45^{\circ}$ with the line $x - 3y + 5 = 0$ and passes through $A$,then its equation is:

The area of the triangle formed by the coordinate axes and the line $px + qy = r$ (where $p, q$ and $r$ are positive real numbers) is $\frac{r^2}{2pq}$. If this area is $\frac{1}{54}$ sq. units, then which of the following is true?

If $P(x_1, y_1)$ and $Q(x_2, y_2)$ are points on $2x + 3y + 1 = 0$ such that $|PA - PB|$ is maximum and $|QA - QB|$ is minimum,where $A(2, 0)$ and $B(0, 2)$,then the value of $x_1 - y_1 + x_2 - y_2$ is -