3. Given the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0), F$ is the right focus of the ellipse, $AB$ is a chord passing through the center $O$, then the maximum value of the area of $\triangle ABF$ is $\qquad$ .
Answer: $b \sqrt{a^{2}-b^{2}}$.
Analysis: Let $E$ be the left focus of the ellipse, $\therefore S_{A B F}=S_{A O F}+S_{B O F}=S_{A O F}+S_{A O E}=S_{A E F} \leq b \sqrt{a^{2}-b^{2}}$.