Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellipse $x^2+4 y^2=4$. If the hyperbola passes through a focus of the ellipse, then
Select ALL correct options:
A
the equation of the hyperbola is $\frac{x^2}{3}-\frac{y^2}{2}=1$
B
a focus of the hyperbola is $(2,0)$
C
the eccentricity of the hyperbola is $\sqrt{\frac{5}{3}}$
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