Given this hyperbola $x_1^2-x_2^2=1$, how do I transform it into $y_1y_2=1$?
When I factor the first equation I get $(x_1+x_2)(x_1-x_2)=1$,
so I thought $y_1=(x_1+x_2)$ and $y_2=(x_1-x_2)$. Therefore the matrix must be $ \begin{pmatrix} 1&1\\1&-1 \end{pmatrix} $.
But in maple it is just drawn as a straight line. However, it should be a rotated hyperbola.
Is my matrix incorrect? And how come $x_1^2-x_2^2=1$ is a hyperbola and $(x_1+x_2)(x_1-x_2)=1$ is a line? Aren't these equations equivalent?
