$\triangle \mathrm{ABC}$ has vertices $\mathrm{A}(-\mathrm{a}, 0)$ and $\mathrm{B}(\mathrm{b}, 0) \quad(\mathrm{a}>0, \mathrm{b}>0)$ fixed, the third vertex is $\mathrm{C}(\mathrm{x}, \mathrm{y})$, if $\mathrm{CO}(\mathrm{O}$ is the origin) is the bisector of $\angle \mathrm{ACB}$, find the equation of the locus of point $\mathrm{C}$.