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JEE Advanced2021MathematicsEllipseActual

Let E be the ellipse x 2 16 + 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 _____.

Correct answer

0

Step-by-step solution

. In a triangle sides joining the mid-points of two sides is half and parallel to third side M 1 M 2 = 1 2 Q Q ' Maximum value of Q Q ' is A A ' Hence, maximum value of M 1 M 2 = 1 2 A A ' = 4

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