  We show that, for all $\alpha\geq 0$, the generalized Grushin plane
$\mathbb{G}_{\alpha}$ is bi-Lipschitz homeomorphic to a $2$-dimensional
quasiplane in the Euclidean space $\mathbb{R}^{[\alpha ]+2}$, where $[\alpha]$
is the integer part of $\alpha$. The target dimension is sharp. This
generalizes a recent result of Wu.
