A curve $C$ has equation $y^2 = x + \mathrm{e}^{2x} y$. Show that \((2y - \mathrm{e}^{2x})

Question

A curve $C$ has equation $y^2 = x + \mathrm{e}^{2x} y$. Show that $(2y - \mathrm{e}^{2x}) \frac{\mathrm{d}y}{\mathrm{d}x} = 1 + 2y\mathrm{e}^{2x}$.[2] Find the equations of the tangents to $C$ at the points where $x = 0$.[4]

Accepted Answer

(b) $y=-x$ and $y=3x+1$

2025 TMJC P1 Q2

2025 TMJC P1 Q2

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