The line passing through the points $(1, 4)$ and $(-5, 1)$ intersects the line $4x + 3y - 5 = 0$ at the point:

If the straight line through the point $P(3, 4)$ makes an angle $\frac{\pi}{6}$ with the $x$-axis and meets the line $12x + 5y + 10 = 0$ at $Q$,then the length $PQ$ is

Reduce the following equation into intercept form and find its intercepts on the axes: $3y + 2 = 0$.

Find the equation of the line passing through the intersection of the lines $y = 3$ and $x + y = 0$ and parallel to the line $2x - y = 4$.

$A$ line $L$ perpendicular to the line $5x - 12y + 6 = 0$ makes a positive intercept on the $Y$-axis. If the distance from the origin to the line $L$ is $2$ units and the angle made by the perpendicular drawn from the origin to the line $L$ with the positive $X$-axis is $\theta$,then $\tan \theta + \cot \theta =$

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