Find the equation of the line passing through the point of intersection of the lines $4x + 7y - 3 = 0$ and $2x - 3y + 1 = 0$ that has equal intercepts on the axes.

Find the equation of the line passing through the point $(1, -2)$ and making equal intercepts on the axes.

$A$ line $L$ passes through the point $P(1, 2)$ and makes an angle of $60^{\circ}$ with the positive $X$-axis. $A$ and $B$ are two points lying on $L$ at a distance of $4$ units from $P$. If $O$ is the origin,then the area of $\triangle OAB$ is

The equation of the line whose slope is $3$ and which cuts off an intercept of $3$ from the positive $x$-axis is

The polar equation of the line perpendicular to the line $\sin \theta - \cos \theta = \frac{1}{r}$ and passing through the point $\left(2, \frac{\pi}{6}\right)$ is

In what ratio does the line $y - x + 2 = 0$ divide the line segment joining the points $(3, -1)$ and $(8, 9)$?