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The normal at a point `P` on the ellipse `x^2+4y^2=16` meets the x-axis at `Qdot` If `M` is the midpoint of the line segment `P Q ,` then the locus of `M` intersects the latus rectums of the given ellipse at points. `(+-((3sqrt(5)))/2+-2/7)` (b) `(+-((3sqrt(5)))/2+-(sqrt(19))/7)` `(+-2sqrt(3),+-1/7)` (d) `(+-2sqrt(3)+-(4sqrt(3))/7)`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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The normal at a point P on the ellipse x^2+4y^2=16 meets the x-axis at Qdot If M is the midpoint of the line segment P Q , then the locus of M intersects the latus rectums of the given ellipse at points. (a) (+-((3sqrt(5)))/2+-2/7) (b) (+-((3sqrt(5)))/2+-(sqrt(19))/7) (c) (+-2sqrt(3),+-1/7) (d) (+-2sqrt(3)+-(4sqrt(3))/7)

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