2010 A-Level H2 Mathematics
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Question 4Applications of Differentiation8 marks
- Given that ${{x}^{2}}-{{y}^{2}}+2xy+4=0$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$.
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- 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.
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Final Answer:
\(\frac{dy}{dx} = \frac{y+x}{y-x}\); points: \((\sqrt{2}, -\sqrt{2})\) and \((-\sqrt{2}, \sqrt{2})\)