$\begin{aligned} & \text { we have } \frac{\mathrm{y}}{\mathrm{x}} \cos ^4 \alpha+\frac{\mathrm{x}}{\mathrm{y}} \sin ^4 \alpha=2 \sin ^2 \alpha \cdot \cos ^2 \alpha \\ & \Rightarrow \mathrm{x}^2 \sin ^4 \alpha+\mathrm{y}^2 \cos ^4 \alpha-2 \mathrm{xy} \sin ^2 \alpha \cos ^2 \alpha=0 \\ & \Rightarrow\left(\mathrm{x} \sin ^2 \alpha-\mathrm{y} \cos ^2 \alpha\right)=0 \\ & \Rightarrow \sin ^2 \alpha-\frac{\mathrm{dy}}{\mathrm{dx}} \cos ^2 \alpha=0 \\ & \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\sin ^2 \alpha}{\cos ^2 \alpha}\end{aligned}$