Let E be the ellipse x216+y29=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

Let E be the ellipse x216+y29=1. For any three distinct points P,Q and

1.	Let E be the ellipse x216+y29=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
Answer» Let $E$ be the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ . 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