I have a question about the hyperbola matrix. In this question, I should find a matrix that is the hyperbola.
I know that if the determinant of a symmetric matrix be less than zero it'll be the hyperbola.
$$M_1=\begin{pmatrix}1&\frac{1}{2}&1\\ \frac{1}{2}& 1 & 1 \\ 1 & 1 & -1\end{pmatrix}\qquad M_2=\begin{pmatrix}0 & 0 & 3 \\ 0 & 1 & 7 \\ 3 & 7 & -1\end{pmatrix}$$