(i)[4]
Show that $2y = 13 - x$ is the equation of the perpendicular bisector of $AB$.
(ii)[5]
The curve intersects the perpendicular bisector of $AB$ at $C$ and $D$. Find, by calculation, the distance $CD$, and give your answer in the form $\sqrt{\left(\frac{p}{q}\right)}$, where $p$ and $q$ are integers.