Find the equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm 2,0)$.

Question

$\begin{array}{1 1}\large\frac{x^2}{5}-\frac{y^2}{4}\normalsize =\large\frac{4}{9}\\\large\frac{y^2}{5}-\frac{x^2}{4}\normalsize =\large\frac{4}{9}\\\large\frac{x^2}{4}-\frac{y^2}{5}\normalsize =\large\frac{4}{9}\\\large\frac{y^2}{4}-\frac{x^2}{5}\normalsize =\large\frac{4}{9}\end{array} $