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:

$A$ line passing through the point $A(-5, -4)$ intersects the lines $x + 3y + 2 = 0$,$2x + y + 4 = 0$,and $x - y - 5 = 0$ at points $B$,$C$,and $D$ respectively. If $\left( \frac{15}{AB} \right)^2 + \left( \frac{10}{AC} \right)^2 = \left( \frac{6}{AD} \right)^2$,find the equation of the line.

If each of the points $(a, 4)$ and $(-2, b)$ lies on the line joining the points $(2, -1)$ and $(5, -3)$,then the point $(a, b)$ lies on the line:

The point $P(a, b)$ lies on the straight line $3x + 2y = 13$ and the point $Q(b, a)$ lies on the straight line $4x - y = 5$. Then the equation of the line $PQ$ is

The equation of a line passing through $(p \cos \alpha, p \sin \alpha)$ and making an angle $(90^\circ + \alpha)$ with the positive direction of the $X$-axis is:

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2,3)$.