Find the distance between the lines $3x + 4y + 7 = 0$ and $3x + 4y + 22 = 0$.

If the points $(1, 2)$ and $(3, 4)$ lie on opposite sides of the line $3x - 5y + a = 0$,then:

The distance between the lines $4x + 3y = 11$ and $8x + 6y = 15$ is:

If the perpendicular distance from the point $(1, 1)$ to the line $3x + 4y + c = 0$ is $7$,then the possible values of $c$ are:

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 $4P_1^2 + P_2^2$?

The base of an equilateral triangle is represented by the equation $2x - y - 1 = 0$ and its vertex is $(1, 2)$. Then,the length (in units) of the side of the triangle is: