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Hyperbola question

2011 · Shift 1 · Q31

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PYQ Library
JEE Advanced
Mathematics
Hyperbola
2011 · Shift 1 · Q31

Hyperbola question

2011 · Shift 1 · Q31

JEE AdvancedMathematicsHyperbolaMultiple correct+4 / −1

Let the eccentricity of the hyperbola

{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1

be reciprocal to that of the ellipse

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

. If the hyperbola passes through a focus of the ellipse, then

A
the equation of the hyperbola is ${{{x^2}} \over 3} - {{{y^2}} \over 2} = 1$
B
a focus of the hyperbola is $(2, 0)$
C
theeccentricity of the hyperbola is $\sqrt {{5 \over 3}}$
D
The equation of the hyperbola is ${x^2} - 3{y^2} = 3$

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