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Ellipse question

2009 · Shift 2 · Q34

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PYQ Library
JEE Advanced
Mathematics
Ellipse
2009 · Shift 2 · Q34

Ellipse question

2009 · Shift 2 · Q34

JEE AdvancedMathematicsEllipseMCQ+3 / −1

The normal at a point

P

on the ellipse

{x^2} + 4{y^2} = 16

meets the

x

- axis

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
$\left( { \pm {{3\sqrt 5 } \over 2},\, \pm {2 \over 7}} \right)$
B
$\left( { \pm {{3\sqrt 5 } \over 2},\, \pm \sqrt {{{19} \over 4}} } \right)$
C
$\left( { \pm 2\sqrt 3 , \pm {1 \over 7}} \right)$
D
$\left( { \pm 2\sqrt 3 , \pm {{4\sqrt 3 } \over 7}} \right)$

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