Question: Let E be the ellipse + x 16 9 = 1. For any three distinct points P, Q and Q' on E, let M(P,

Let E be the ellipse + x 16 9 = 1. For

Let E be the ellipse + x 16 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

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