  In this short note, we show that any rational curve passing through the
generic point in a moduli space of stable bundles with rank $r$ and fixed
determinant on a smooth projective curve of genus $g\ge 4$ has degree (with
respect to the anti-canonical line bundle of the moduli space) at least $2r$.
It has degree $2r$ if and only if it is a Hecke curve.
