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

The normal at a point P on the ellipse `x^(2)+4y^(2)=16` meets the x-axisat 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

`(pm (3 sqrt(5))/(2), pm (2)/(7))`

B

`(pm (3 sqrt(5))/(2), pm (sqrt(19))/(4))`

C

`(pm 2 sqrt(3), pm (1)/(7))`

D

`(pm 2 sqrt(3), pm (4 sqrt(3))/(7))`

Text Solution

Verified by Experts

The correct Answer is:
C
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