  The presence of slow-fast Hopf (or singular Hopf) points in slow-fast systems
in the plane is often deduced from the shape of a vector field brought into
normal form. It can however be quite cumbersome to put a system in normal form.
In the monograph "Canards from birth to transition", an intrinsic presentation
of slow-fast vector fields is initiated, showing hands-on formulas to check for
the presence of such singular contact points. We generalize the results in the
sense that the criticality of the Hopf bifurcation can be checked with a single
formula. We demonstrate the result on a slow-fast system given in non-standard
form where slow and fast variables are not separated from each other. The
formula is convenient since it does not require any parameterization of the
critical curve.
