What is the square root of the sum of the squares of the lengths of the perpendiculars drawn from the point $(-3, 4)$ to both axes?

In what ratio does the point $(8, 4)$ divide the line segment joining the points $(5, -2)$ and $(9, 6)$?

The ratio in which the straight line $3x + 4y = 6$ divides the join of the points $(2, -1)$ and $(1, 1)$ is

If the midpoint of the line segment joining the points $(5, a)$ and $(b, 7)$ is $(3, 5)$,find $(a, b)$.

Two particles $P$ and $Q$ located at the points with coordinates $P(t, t^3-16t-3)$ and $Q(t+1, t^3-6t-6)$ are moving in a plane. The minimum distance between them in their motion is

Find the distance between the points $P \left( 3, -\frac{\pi}{6} \right)$ and $Q \left( 4, \frac{\pi}{3} \right)$ in polar coordinates.