If the slope of a line is $2$ and it makes an intercept of $-4$ on the $y$-axis,then its equation is:

The equation of the line perpendicular to $x = c$ is

The equations of the lines which make intercepts on the axes whose sum is $8$ and product is $15$ are

The equation of the line passing through $(1, 2)$ and perpendicular to $3x + 4y + 5 = 0$ is

The line passing through $(-1, \pi/2)$ and perpendicular to $\sqrt{3} \sin \theta + 2 \cos \theta = \frac{4}{r}$ is

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