A point charge (-q) placed at the point A, as shown in the following figure, is

If the potential energy of the system is minimum, this will be stable equilibrium. 

for stable equilibrium, 

$\frac{\mathrm{dU}}{\mathrm{dx}}=0 \& \frac{{\mathrm{d}}^2\mathrm{U}}{{\mathrm{dx}}^2}>0$

for unstable equilibrium,

$\frac{\mathrm{dU}}{\mathrm{dx}}=0 \& \frac{{\mathrm{d}}^2\mathrm{U}}{{\mathrm{dx}}^2}<0$

Also, if -ve charge is placed at A, it will oscillate along y-axis if displaced slightly, but it will move towards the direction along x-axis if is displaced slightly.

so, it will be in stable equilibrium along y-axis while it will be in unstable equilibrium along x-axis.