What are the Cartesian coordinates of $(2, \pi /4)$?

If the distance between the points $(a, 2)$ and $(3, 4)$ is $8$,then $a = $

If the coordinates of the vertices of $\Delta OAB$ are $(0, 0)$,$(\cos \alpha, \sin \alpha)$,and $(-\sin \alpha, \cos \alpha)$ respectively,then $OA^2 + OB^2 = $

If the polar coordinates of a point are $(2, \pi /3)$,find its Cartesian coordinates.

The points $A(1, 1)$,$B(-2, 7)$,and $C(3, -3)$ are . . . . . . .

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} = $