Circle passing through $(3,4),(3,2),(1,4)$
$$
\begin{aligned}
& \mathrm{S}+\lambda \mathrm{L}=0 \\
& (x-3)(x-3)+(y-4)(y-2)+\lambda[(x-3)]=0
\end{aligned}
$$

It passes through $(1,4)$
$$
\begin{aligned}
& \therefore(1-3)^2+(4-4)(4-2)+\lambda(1-3)=0 \\
& \lambda=2
\end{aligned}
$$
$\therefore$ Equation of circle is
$$
\begin{aligned}
& (x-3)^2+(y-4)(y-2)+2(x-3)=0 \\
& x^2-6 x+9+y^2-6 y+8+2 x-6=0 \\
& x^2+y^2-4 x-6 y+11=0 \\
& \text { clearly centre } \equiv(2,3) \\
& \text { radius }=\sqrt{2}
\end{aligned}
$$
$\therefore$ parametric equation
$$
\begin{aligned}
& x=2+\sqrt{2} \cos \theta ; \quad y=3+\sqrt{2} \sin \theta \\
& a=2, r=\sqrt{2} \\
& b=3 \\
& b^a \cdot r^a=3^2 \cdot(\sqrt{2})^2=18
\end{aligned}
$$