What starting conditions for two harmonic oscillators will cause an elliptic path?

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I have the two following equations:

$$y(t) = A\cos \left( \sqrt\frac{2k}{m}t-\phi_y \right)$$

$$x(t) = B\cos \left( \sqrt\frac{2k}{m}t-\phi_x \right)$$

I need to find the starting conditions so that the "curves" will move in an ellipse, where it's main axis is on one of the major axis $(x,y)$.

I'd appreciate a hint. I understand it has to do something with $\phi_{x,y}$, but I can't seem to find anything related at the moment.