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