(A) Given the parametric equations: $x = at^2$ and $y = 2at$. Differentiating $x$ with respect to $t$: $\frac{dx}{dt} = \frac{d}{dt}(at^2) = 2at$. Dif

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(A) Given the parametric equations: $x = at^2$ and $y = 2at$. Differentiating $x$ with respect to $t$: $\frac{dx}{dt} = \frac{d}{dt}(at^2) = 2at$. Differentiating $y$ with respect to $t$: $\frac{dy}{dt} = \frac{d}{dt}(2at) = 2a$. Using the chain rule for parametric differentiation: $\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{2a}{2at} = \frac{1}{t}$.

Class 12 Mathematics Continuity and Differentiability Derivatives of Functions in Parametric Forms

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Find $\frac{dy}{dx}$,if $x = at^2$ and $y = 2at$.

A
$\frac{1}{t}$
B
$t$
C
$2t$
D
$\frac{1}{2t}$

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Continuity and Differentiability

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Derivatives of Functions in Parametric Forms

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Find $\frac{dy}{dx}$,if $x = at^2$ and $y = 2at$.

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