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

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of set $A$ is $56$ more than the total number of subsets of set $B$. Then the distance of the point $P(m, n)$ from the point $Q(-2, -3)$ is

What are the coordinates of the points of trisection of the line segment joining the points $(-3, -3)$ and $(6, 6)$?

The ratio in which the $x$-axis divides the line segment joining the points $(2, -3)$ and $(5, 6)$ is

What is the distance between the points $(2, 15^{\circ})$ and $(1, 75^{\circ})$ in polar coordinates?

Consider three points $P = (-\sin(\beta - \alpha), -\cos \beta)$,$Q = (\cos(\beta - \alpha), \sin \beta)$,and $R = (\cos(\beta - \alpha + \theta), \sin(\beta - \theta))$,where $0 < \alpha, \beta, \theta < \frac{\pi}{4}$. Then: