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The normal at a point P, on the ellipse ...

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-rectum of the given ellipse at the points :

A

`(+- (3 sqrt5)/2, +-2/7)`

B

`(+- (3 sqrt5)/2, +-sqrt19/4)`

C

`(+-2sqrt3, +-1/7)`

D

`(+-2 sqrt3, +-(4sqrt3)/7)` .

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