How is the equation $z=xy$ a hyperbolic paraboloid?

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The general equation for a hyperbolic paraboloid is $z - z_{0} = \frac{(x - x_{0})^{2}}{a^{2}} -\frac{(y - y_{0})^{2}}{b^{2}}$. How is the equation $z=xy$ a hyperbolic paraboloid? Is there any algebra that can be applied to it to get its general form?

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