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

The distance of the point $(b \cos \theta, b \sin \theta)$ from the origin is

Let $A = (a_1, a_2)$ and $B = (b_1, b_2)$ be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between $A$ and $B$?

If the coordinates of two opposite vertices of a square are $(a, b)$ and $(b, a)$,find the area of the square.

If the point $M(x, y)$ divides the line segment joining $A(b \cos \alpha, b \sin \alpha)$ and $B(a \cos \beta, a \sin \beta)$ in the ratio $b:a$,then $x \cos \frac{\alpha + \beta}{2} + y \sin \frac{\alpha + \beta}{2} = $

The line $x + y = 4$ divides the line segment joining the points $(-1, 1)$ and $(5, 7)$ in the ratio: