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If $x$ and $y$ are connected parametrically by the equations given in $ x = 2at^2, \: y = at^4 $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$

$\begin{array}{1 1} t \\ t^2 \\ t^3 \\ 0 \end{array} $

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1 Answer

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Toolbox:
  • $\large\frac{dy}{dx}=\frac{g'(t)}{f'(t)}$
  • $\large\frac{dy}{dt}$$=g'(t)$
  • $\large\frac{dx}{dt}$$=f'(t)$ [Provided $f'(t)\neq 0$]
Step 1:
$x=2at^2$
$f'(t)=\large\frac{dx}{dt}$$=4at$
Step 2:
$y=at^4$
$g'(t)=\large\frac{dy}{dt}$=$4at^3$
Step 3:
$\large\frac{dy}{dx}=\frac{g'(t)}{f'(t)}$
$\large\frac{dy}{dx}=\frac{dy}{dt}$$\times \large\frac{dt}{dx}$
$\quad\;=4at^3\times \large\frac{1}{4at}$
$\quad\;=t^2$
answered May 9, 2013 by sreemathi.v
 

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