Ans: A
Note that the coordinates of the circumcentre are $\left(\dfrac{a}{2}, \dfrac{b}{2} \right)$.
Sub. $\left(\dfrac{a}{2}, \dfrac{b}{2} \right)$ into $4x+16y=17a$, we have
$\begin{array}{rcl}
4 \left( \dfrac{a}{2} \right) +16\left(\dfrac{b}{2} \right) & = & 17a \\
2a +8b & = & 17a \\
8b & = & 15a \\
\dfrac{a}{b} & = & \dfrac{8}{15} \\
a:b & = & 8:15
\end{array}$
