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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
the equation of the hyperbola is $$\frac{x^2}{3} - \frac{y^2}{2} = 1$$ a focus of the hyperbola is (2, 0)
a focus of the hyperbola is (2, 0)
the eccentricity of the hyperbola is $$\sqrt{\frac{5}{3}}$$
the equation of the hyperbola is $$x^2 - 3y^2 = 3$$
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