The end points of the diameter of a circle are $(2, 4)$ and $(2, 6)$. The radius of the circle is:

The distance of point $A(a \cos \theta, a \sin \theta)$ from the origin is $\ldots \ldots \ldots \ldots$ $(a \in R^{+})$

State whether the following statement is true or false. Justify your answer.
The points $A(-1, -2)$,$B(4, 3)$,$C(2, 5)$,and $D(-3, 0)$ in that order form a rectangle.

State whether the following statement is true or false. Justify your answer.
Points $A(3, 1)$,$B(12, -2)$,and $C(0, 2)$ cannot be the vertices of a triangle.

If $P(\frac{a}{3}, 4)$ is the mid-point of the line segment joining the points $Q(-6, 5)$ and $R(-2, 3)$,then the value of $a$ is

The fourth vertex $D$ of a parallelogram $ABCD$ whose three vertices are $A(-2,3)$,$B(6,7)$,and $C(8,3)$ is