Let x=9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is 1/3. Let P (α, 0), α>0, be a focus of E and AB be a chord…

Let $\displaystyle x=9$ be a directrix of an ellipse E , whose centre is at the origin and eccentricity is $\displaystyle \frac{1}{3}$. Let $\displaystyle \mathrm{P}(\alpha, 0)$, $\displaystyle \alpha>0$, be a focus of E and AB be a chord passing through P. Then the locus of the mid point of AB is :