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QJEEAdv21Ma3dec: JEE Advanced 2021 Mathematics - Class 11 JEEAdv21Ma3dec Solution: Let E be the ellipse x 2 16 + y 2 9 = 1 . For any three…

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 _______.

Step-by-Step Verified Solution

As we know that, in a triangle, sides joining the mid-points of two sides is half and parallel to the third side.

∴ M1M2=12QQ′

JEE Advanced 2021 Paper 2 Online Mathematics - Ellipse Question 4 English Explanation
Maximum value of QQ' is AA'

Hence, maximum value of M1M2=12AA′=4

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