9. (16 points) Given the parabola $y=x^{2}$ and the ellipse $(x-3)^{2}+4 y^{2}=1$, the focus of the parabola is $F$, and $A$ is a point on the ellipse. The line $F A$ intersects the parabola at points $B$ and $C$. Tangents to the parabola are drawn through points $B$ and $C$. Find the locus of the intersection of the two tangents.