Find d y d x if, : x = a t ^2, y =2 at - Vidyadip

Question

Find $\frac{d y}{d x}$ if, :
$
x = a t ^2, y =2 at
$

✓

Answer

$
x = at { }^2, y =2 at
$
Differentiating $x$ and $y$ w.r.t. $t$, we get
$
\frac{d x}{d t}=a \frac{d}{d t}\left(t^2\right)=a \times 2 t=2 a t
$
$
\begin{aligned}
& \text { and } \frac{d y}{d t}=2 a \frac{d}{d t}(t)=2 a \times 1=2 a \\
& \therefore \frac{d y}{d x}=\frac{(d y / d t)}{(d x / d t)}=\frac{2 a}{2 a t}=\frac{1}{t} .
\end{aligned}
$

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