Q 1  If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the  parameter, Find dy/dx .

         x = 2at^2, y = at^4

Answers (1)

Given equations are
x = 2at^2, y = at^4
Now, differentiate both w.r.t  t
We get,
\frac{dx}{dt}=\frac{d(2at^2)}{dt}= 4at
Similarly,
\frac{dy}{dt}=\frac{d(at^4)}{dt}= 4at^3
Now, \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}= \frac{4at^3}{4at} = t^2
Therefore, the answer is \frac{dy}{dx}= t^2

 

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