JEE Advanced 2021 · Paper 2, Mathematics question 18

Let $E$ be the ellipse $\dfrac{x^2}{16} + \dfrac{y^2}{9} = 1$. For any three distinct points $P$, $Q$ and $Q'$ on $E$, let $M(P, Q)$ be the mid-point of the line segment joining $P$ and $Q$, and $M(P, Q')$ be the mid-point of the line segment joining $P$ and $Q'$. Then the maximum possible value of the distance between $M(P, Q)$ and $M(P, Q')$, as $P$, $Q$ and $Q'$ vary on $E$, is ____.