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let the eccentricity of the hyperbola `x^2/a^2-y^2/b^2=1` be reciprocal to that of the ellipse `x^2+4y^2=4.` if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is `x^2/3-y^2/2=1` (b) a focus of the hyperbola is `(2,0)` (c) the eccentricity of the hyperbola is `sqrt(5/3)` (d) the equation of the hyperbola is `x^2-3y^2=3`

A

the equation of hyperbola is `(x^(2))/(3)-(y^(2))/(2)=1`

B

a focus of the hyperbola is `(2, 0)`

C

the eccentricity of the hyperbola is `sqrt((5)/(2))`

D

the equation of the hyperbola is `x^(2)-3y^(2)=3`

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The correct Answer is:
B, D
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