Question

If $x=a{t}^2,y=2at$, then find $\frac{dy}{dx}$.

Answer 1

We have,

$x=a{t}^2$
and $y=2at$
$\therefore \frac{dx}{dt}=2at$
and $\frac{dy}{dt}=2a$
$\therefore \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{2a}{2at}=\frac{1}{t}$.