The normal to a given curve is parallel to x - axis, if

$\frac{d y}{d x}=0$ $\frac{d y}{d x}=1$ $\frac{d x}{d y}=0$ $\frac{d x}{d y}=1$

$\frac{d x}{d y}=0$

We have, Slope of the normal = 0 $\Rightarrow-\frac{d x}{d y}=0 \Rightarrow \frac{d x}{d y}=0$