2010 TYS

Given that ${{x}^{2}}-{{y}^{2}}+2xy+4=0$, find $\frac{\text{d}y}{\text{d}x}$ in terms of $x$ and $y$.

For the curve with equation ${{x}^{2}}-{{y}^{2}}+2xy+4=0$, find the coordinates of each point at which the tangent is parallel to the $x$-axis.