The Learning Rate a Ravine Allows

A ravine-shaped loss — steep across, gentle along:

$L(x,y) = 10x^2 + 0.5y^2$

Gradient descent uses the same learning rate $\alpha$ on both coordinates:

$x \leftarrow x - \alpha \frac{\partial L}{\partial x}, \qquad y \leftarrow y - \alpha \frac{\partial L}{\partial y}$

Starting from $(1,\,1)$, above which value of $\alpha$ does $|x|$ grow from one step to the next instead of shrinking, sending training off to infinity?