If x = at^2 and y = 2at,then frac{dy}{dx} = | vedclass

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Question

(D) Given parametric equations are $x = at^2$ and $y = 2at$.First,differentiate $x$ with respect to $t$:$\frac{dx}{dt} = \frac{d}{dt}(at^2) = 2at$.Nex

Vedclass · Accepted Answer

$\frac{1}{t}$

Vedclass · Answer

(D) Given parametric equations are $x = at^2$ and $y = 2at$.First,differentiate $x$ with respect to $t$:$\frac{dx}{dt} = \frac{d}{dt}(at^2) = 2at$.Next,differentiate $y$ with respect to $t$:$\frac{dy}{dt} = \frac{d}{dt}(2at) = 2a$.Using the chain rule for parametric differentiation:$\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{2a}{2at}$.Since $t 
eq 0$ and $a 
eq 0$,we simplify the expression:$\frac{dy}{dx} = \frac{1}{t}$.Therefore,the correct option is $D$.

If $x = at^2$ and $y = 2at$,then $\frac{dy}{dx} =$ . . . . . . ,where $t \neq 0$.

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