Mathematics - Ellipse Question with Solution | TestHub

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