Quadratic Form Induces Riemannian Metric?

I feel like somehow the form x2 -y2 is associated to the hyperbolic plane, but I do not know in what way. Generalizing this, I feel like a quadratic form on Rn should induce a Riemannian Metric, in such a way that the standard quadratic form induces the standard RM on Rn. Is all/any of this right?

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Nevin Manimala

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