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Question
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = 2at2, y = at4
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Solution
Given, x = 2at2 ....(i)
and y = at4 ....(ii)
Differentiating (i) and (ii) w.r.t. t, we get
`dx/dt = 2a d/dt (t^2)`
= 2a × 2t
= 4at
And `dy/dt = a d/dt t^4`
= a × 4t3
= 4at3
∴ `dy/dx = (dy/dt)/(dx/dt)`
= `(4at^3)/(4at)`
= t2
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