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2014-10-08T14:02:53+05:30

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x=a t^{2}

Differenciating x with respect to t, we get

 \frac{dx}{dt} = \frac{d}{dt} (at^{2} )=2at

y=2at

Differentiating y with respect to t, we get

 \frac{dy}{dt} = \frac{d}{dt} (2at)=2a

 \frac{dy}{dx}= \frac{( \frac{dy}{dt})}{( \frac{dx}{dt})}   = \frac{2a}{2at} = \frac{1}{t}

2 4 2
2014-10-08T14:32:55+05:30

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We can get dy/dx in many ways.

x = at^2,\ \ \ \ y=2at\\ \\x=a(y/2a)^2=\frac{y^2}{4a}\\ \\y^2=4ax\\ \\Differentiating\ \ wrt\ \ x\\ \\2y. \frac{dy}{dx}= 4a\\ \\\frac{dy}{dx}=\frac{2a}{y}=\frac{2a}{2at}=\frac{1}{t}\\

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