Solution (source code)

= Solution

At the downward vertical equilibrium, the lower spring supports $m_2g$ and the upper spring supports $(m_1+m_2)g$. Thus the <two vertically suspended springs> have lengths
$$
L_2=\ell+\frac{m_2g}{k_2},\qquad
L_1=\ell+\frac{(m_1+m_2)g}{k_1},
$$
and positions
$$
\boxed{(x_1,y_1)=(0,-L_1),\qquad
(x_2,y_2)=(0,-L_1-L_2).}
$$