JEE Advance - Mathematics (2021 - Paper 2 Online - No. 18)
Let E be the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1$$. 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 _______.
Answer
4
Explanation
As we know that, in a triangle, sides joining the mid-points of two sides is half and parallel to the third side.
$$\therefore$$ $${M_1}{M_2} = {1 \over 2}QQ'$$
Maximum value of QQ' is AA'
Hence, maximum value of $${M_1}{M_2} = {1 \over 2}AA' = 4$$
$$\therefore$$ $${M_1}{M_2} = {1 \over 2}QQ'$$
Maximum value of QQ' is AA'
Hence, maximum value of $${M_1}{M_2} = {1 \over 2}AA' = 4$$
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