The hyperbola `(y^(2))/(a^(2))-(x^(2))/(b^(2)) =1` passes through the points `(0, -2)` and `(sqrt(3). 4)` . Find the value of e i.e., the eccentricity of the given hyperbola.

Explanation

To find the eccentricity \( e \) of the hyperbola given by the equation

\[ \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \]

which passes through the points \( (0, -2) \) and \( (\sqrt{3}, 4) \), we will follow these steps:

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