Step-by-step Solution:

the eccentricity is given by: \[ e^2 = 1 - \frac{b^2}{a^2}. \] Substitute the given value for \( e^2 \): \[ 1 - \frac{b^2}{a^2} = \frac{1}{9} \quad \Rightarrow \quad \frac{b^2}{a^2} = \frac{8}{9}. \] The equation of the directrix is given by: \[ x = \pm \frac{a}{e} = \pm 3a. \] Given that one of the directrices is \( x = 9 \), we have: \[ 3a = 9 \quad \Rightarrow \quad a = 3. \] Now, using \( a = 3 \), we find: \[ b^2 = 8. \] Thus, the equation of the ellipse is: \[ \frac{x^2}{9} + \frac{y^2}{8} = 1. \]