Question

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

Answer 1

$x=a{t}^2$

$\frac{dx}{dt}=a\left(2t\right)=2at$

$y=2at$

$\frac{dy}{dt}=2a$

$\therefore \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{2a}{2at}=\frac{1}{t}$

We have $y=2at$

$\Rightarrow t=\frac{y}{2a}\Rightarrow \frac{1}{t}=\frac{2a}{y}$

$\therefore \frac{dy}{dx}=\frac{1}{t}$

Hence $\frac{dy}{dx}=\frac{2a}{y}$