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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(3sqrt5/2,pm2/7)`

B

`(pm(3sqrt5/2,pmsqrt19/4)`

C

`(pm2sqrt3,pm1/7)`

D

`(pm2sqrt3,pm(4sqrt3/7)`

Text Solution

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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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ARIHANT MATHS ENGLISH-ELLIPSE-Exercise (Questions Asked In Previous 13 Years Exam)
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  12. Statement 1: An equation of a common tangent to the parabola y^2=16s...

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  13. An ellipse is drawn by taking a diameter of the circle (x-1)^2+y^2=1 ...

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