Eigenvectors of 2x2 matrix shortcut

[wil3]

Hello. I recall from Linear Algebra there being an ultra-fast shortcut for finding the eigenvectors of a 2x2 matrix after finding the eigenvalues. Does anyone know what it is? I remember it being mentioned in passing in Strang's wonderful textbook, but I cannot find it now.

I'm aware of the standard kernel method. I'm looking for the shortcut here only. It's a trick that only works for 2x2 matrices.

Thanks very much!