9. Given the ellipse
$$
\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)
$$

with an eccentricity of $\frac{\sqrt{3}}{2}$, a line with a slope of 1 passing through the point $M(b, 0)$ intersects the ellipse at points $A$ and $B$. Let $O$ be the origin. If
$$
\overrightarrow{O A} \cdot \overrightarrow{O B}=\frac{32}{5} \cot \angle A O B,
$$

then the equation of the ellipse is $\qquad$