9. A circle passes through the intersection points of the circles $(x-1)^{2}+(y-2)^{2}=6$ and $(x-2)^{2}+(y+1)^{2}=8$ and the origin. Find the equation of this circle.
9. Let the equation of the required circle be $(x-1)^{2}+(y-2)^{2}-6+\lambda\left[(x-2)^{2}+(y+1)^{2}-8\right]=0$. Since it passes through the origin $(0,0)$, substituting gives $\lambda=-\frac{1}{3}$. Thus, the equation of the required circle is $x^{2}+y^{2}-x-7 y=0$.