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

Options

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) = 2`

Answer

B