If x and y are connected parametrically by th | vedclass

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Question

(A) Given the parametric equations: $x = 2at^{2}$ $y = at^{4}$ First,differentiate $x$ with respect to $t$: $\frac{dx}{dt} = \frac{d}{dt}(2at^{2}) = 2

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$t^{2}$

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(A) Given the parametric equations: $x = 2at^{2}$ $y = at^{4}$ First,differentiate $x$ with respect to $t$: $\frac{dx}{dt} = \frac{d}{dt}(2at^{2}) = 2a \cdot (2t) = 4at$ Next,differentiate $y$ with respect to $t$: $\frac{dy}{dt} = \frac{d}{dt}(at^{4}) = a \cdot (4t^{3}) = 4at^{3}$ Now,find $\frac{dy}{dx}$ using the chain rule: $\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{4at^{3}}{4at} = t^{2}$

If $x$ and $y$ are connected parametrically by the equations,without eliminating the parameter,find $\frac{dy}{dx}$ for $x=2at^{2}$ and $y=at^{4}$.

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