2025 SAJC P1 Q8

A curve has equation \((x - y)^2 = 2\mathrm{e}^{xy}\).

1. Show that \(\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{x - y - y\mathrm{e}^{xy}}{x - y + x\mathrm{e}^{xy}}\).[3]
2. Given that the curve cuts the positive \(y\)-axis at point \(A\), find the equation of the normal to the curve at \(A\).[2]
3. The normal to the curve at \(A\) meets the curve at another point \(B\). Find the coordinates of \(B\).[3]