Find the distance between the lines $5x + 12y + 13 = 0$ and $5x + 12y - 9 = 0$.

What is the perpendicular distance of the line $3x + 4y = 10$ from the origin?

The distance of the point $(2, 3)$ from the line $2x - 3y + 28 = 0$,measured parallel to the line $\sqrt{3}x - y + 1 = 0$,is equal to

The perpendicular distance of the straight line $12x + 5y = 7$ from the origin is equal to

The perpendicular distance from the point $(1, \pi)$ to the line joining $(1, 0^{\circ})$ and $(1, \frac{\pi}{2})$ (in polar coordinates) is

If $P_1$ and $P_2$ are the lengths of the perpendiculars from the origin to the lines $x \sec \theta + y \csc \theta = a$ and $x \cos \theta - y \sin \theta = a \cos 2\theta$ respectively,then what is the value of $4P_1^2 + P_2^2$?