Let $x=9$ be a directrix of an ellipse $E$, whose centre is at the origin and eccentricity is $\frac{1}{3}$. Let $P(\alpha ,0),\alpha 0$, be a focus of $E$ and $A B$ be a chord passing through $P$. Then the locus of the mid-point of $AB$ is: [JEE Main 2026, 6 Apr (Shift 2)]

Question

Let $x=9$ be a directrix of an ellipse $E$, whose centre is at the origin and eccentricity is $\frac{1}{3}$. Let $P(\alpha ,0),\alpha >0$, be a focus of $E$ and $A B$ be a chord passing through $P$. Then the locus of the mid-point of $AB$ is: [JEE Main 2026, 6 Apr (Shift 2)]

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Let \(x=9\) be a directrix of an ellipse \(E\), whose centre is at the origin and eccentricity is \(\frac{1}{3}\). Let \…

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