Find the length of the perpendicular drawn from the point $(2, 1)$ to the line $3x - 4y + 8 = 0$.

If the length of the perpendicular from the origin to the line $x/a + y/b = 1$ is $p$,then which of the following is true for $a^2, 4p^2, b^2$?

An equilateral triangle is constructed between the lines $\sqrt{3} x+y-6=0$ and $\sqrt{3} x+y+9=0$ with the base on one line and the vertex on the other. The area (in sq. units) of the triangle so formed is

Identify the point on the line $2x + 3y + 7 = 0$,which is at a distance of $3$ units from $(1, -3)$.

If the length of the perpendicular drawn from the origin to the line whose intercepts on the axes are $a$ and $b$ is $p$,then

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 $4P_1^2 + P_2^2$?