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JEE Advanced 2021Paper 2
Exam
JEE Advanced
Year
2021
Paper
Paper 2
Subject
Mathematics
Chapter
Ellipse

JEE Advanced 2021 · Paper 2 · Mathematics · Ellipse

Let E be the ellipse x ^ 2 16 + y ^ 2 9 = 1 . For any three...

Let EE be the ellipse x216+y29=1\dfrac{{x}^{2}}{16} + \dfrac{{y}^{2}}{9} = 1. For any three distinct points P,QandP, Q and{Q}^{'}ononE,let, letM(P,Q)M\left(P, Q\right) be the mid-point of the line segment joining PP and QQ, and M\left(P, {Q}^{'}\right)$ be the mid-point of the line segment joining $P$ and ${Q}^{'}$. Then the maximum possible value of the distance betweenM\left(P, Q\right)andandM\left(P, {Q}^{'}\right),as, asP, Qandand{Q}^{'}varyonvary onE$, is _____.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

Correct answer

0

Step-by-step solution

.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

In a triangle sides joining the mid-points of two sides is half and parallel to third side

M1M2=12QQ′{M}_{1}{M}_{2} = \dfrac{1}{2}Q{Q}^{'}

Maximum value of QQ′Q{Q}^{'} is AA′A{A}^{'}

Hence, maximum value of M1M2=12AA′=4{M}_{1}{M}_{2} = \dfrac{1}{2}A{A}^{'} = 4

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