Let the eccentricity of the hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ 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 $$\frac{x^2}{3} - \frac{y^2}{2} = 1$$ a focus of the hyperbola is (2, 0)

B

a focus of the hyperbola is (2, 0)

C

the eccentricity of the hyperbola is $$\sqrt{\frac{5}{3}}$$

D

the equation of the hyperbola is $$x^2 - 3y^2 = 3$$