$\text{If\hspace{0.17em}}x=a{t}^2,y=2at\text{\hspace{0.17em}then \hspace{0.17em}}\frac{dy}{dx}=\frac{\lambda }{t},\lambda =$

$\begin{array}{l}x=a{t}^2\Rightarrow \frac{dx}{dt}=2at\text{ and }y=2at\Rightarrow \frac{dy}{dt}=2a\\ \text{ Hence, the derivative is }\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{2a}{2at}=\frac{1}{t}\Rightarrow \lambda =1\end{array}$