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

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