**Question: **Find $\frac{d y}{d x}$, when

$x=a t^{2}$ and $y=2 a t$

**Solution:**
We have, $x=a t^{2}$ and $y=2 a t \Rightarrow \frac{d x}{d t}=2 a t$ and $\frac{d y}{d t}=2 a \therefore \frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{2 a}{2 a t}=\frac{1}{t}$