The polar coordinates of the point whose Cartesian coordinates are $(-2, -2)$ are given by

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

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:

In what ratio does the line $2x + 3y + 7 = 0$ divide the line segment joining the points $(3, 4)$ and $(7, 8)$?

If $P, Q, R$ are collinear points such that $P(7, 7)$,$Q(3, 4)$ and $PR = 10$,then what are the coordinates of $R$?

Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $x$-axis.