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$Let P (x_{1}, y_{1}) and Q (x_{2}, y_{2}), y_{1} < 0, y_{2} < 0, be the endpoints of the latus rectum of the ellipse x^{2} + 4 y^{2} = 4 . The$
$equations of parabolas with latus rectum P Q are$

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a

x2+23y=3+3

b

x2−23y=3+3

c

x2+23y=3−3

d

x2−23y=3−3

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detailed solution

Correct option is B

The given ellipse isx24+y21=1b2=a21−e2or e=32 Hence, the endpoints P and Q of the latus rectum are given byP≡3,-12and Q≡−3,−12The coordinates of the midpoint of PQ areR≡0,−12 Length of latus rectum, PQ=23 Hence, two parabolas are possible whose vertices are S0,32-12 and T0,−32−12The equation of the parabolas arex2=23y+32+12and x2=−23y−32+12or x2−23y=3+3or x2+23y=3−3

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