Let E be the ellipse frac{x^2}{16}+frac{y^2}{ | vedclass

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(C) Let $A = M(P, Q)$ and $B = M(P, Q^{\prime})$.By the midpoint formula,$A = \frac{P+Q}{2}$ and $B = \frac{P+Q^{\prime}}{2}$.The distance between $A$

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$4$

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(C) Let $A = M(P, Q)$ and $B = M(P, Q^{\prime})$.By the midpoint formula,$A = \frac{P+Q}{2}$ and $B = \frac{P+Q^{\prime}}{2}$.The distance between $A$ and $B$ is given by $|A - B| = |\frac{P+Q}{2} - \frac{P+Q^{\prime}}{2}| = |\frac{Q - Q^{\prime}}{2}| = \frac{1}{2} |Q - Q^{\prime}|$.Here,$|Q - Q^{\prime}|$ represents the distance between two points $Q$ and $Q^{\prime}$ on the ellipse $E$.The maximum distance between any two points on the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ is the length of the major axis.The major axis length is $2a = 2 	imes 4 = 8$.Therefore,the maximum value of $|Q - Q^{\prime}|$ is $8$.Thus,the maximum distance between $M(P, Q)$ and $M(P, Q^{\prime})$ is $\frac{8}{2} = 4$.

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