If the distance between the points $(x, 2)$ and $(3, 4)$ is $2$,find the value of $x$.

The coordinates of the point of trisection of the line segment joining the points $(-2, 3)$ and $(3, -1)$ that is nearer to $(-2, 3)$ are

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 coordinates of the point that divides the line segment joining the points $(-3, 2)$ and $(3, -4)$ internally in the ratio $3 : 2$.

Write the equations for the $x$-axis and $y$-axis.

If the line $2x - y - 4 = 0$ divides the line segment joining the points $(2, -1)$ and $(1, -4)$ at the point $(a, b)$ in the ratio $m:n$,then $4(a - b(\frac{m}{n})^2) = $