Question

Find \[\frac{dy}{dx}\], when \[x = a t^2 \text{ and } y = 2\ at \] ?

Answer 1

\[\text{We have, x } = a t^2 \text{ and } y = 2at\]

\[ \Rightarrow \frac{dx}{dt} = 2at \text{ and } \frac{dy}{dt} = 2a\]

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