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The normal at a point P on the ellipse `x^(2) +4y^(2)=16` meets the x-axis at Q. If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectums of the given ellipse at the points

A

`(pm (3 sqrt5)/(2) , pm (2)/(7))`

B

`(pm (3 sqrt5)/(2), pm (sqrt19)/(4))`

C

`(pm 2 sqrt3, pm (1)/(7))`

D

`(pm 2 sqrt3, pm (4 sqrt3)/(7))`

Text Solution

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The correct Answer is:
C
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