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Question
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx`
`x = 2at^2, y = at^4`
Solution
Given, x = 2at2 and y = at4
Differentiating both sides with respect to,
`dx/dt = 2a d/dx (t^2) = 4at` and `dy/dt = a d/dt t^4 = 4at^3`
Hence, `dy/dx = (dy/dt)/(dx/dt) = (4at^3)/(4at) = t^2`
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