Problem

Part II Fill in the blanks

12. Let $C$ be a variable path in the $xy$-plane of arc-length $1$ starting at the point $(\sqrt{3},1)$ and ending at the point $(a,b)$. Suppose that $G(a,b):=\int_C \sqrt{f}\,dr$, where $f(x,y):=\arctan\frac{y}{x}$ is a function in $a$ and $b$. Then, $G$ attains its maximum at $a=\underline{\quad(14)\quad}$ and $b=\underline{\quad(15)\quad}$, and the maximum value of $G$ is $\underline{\quad(16)\quad}$.