Finding the curvature of a hyperbola

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Think of a hyperbolic paraboloid in a $3D$ graph. When you cut this shape with several $z$ planes such as $z=0$, $z=\pm 1$, $z=\pm2$, we will have several level curves which are hyperbolas. So my question is how can I find the curvature of a hyperbola? I am asking this because I think we can arrive at a conclusion about the general shape by finding the consecutive curvatures of several hyperbolas. Am I right or is it nonsense?