If x and y are connected parametrically by the equations given, without eliminating the parameter, Find `(dy)/(dx)`.
`x=2a t^2, y=a t^4`

Explanation

To find \(\frac{dy}{dx}\) for the parametric equations \(x = 2a t^2\) and \(y = a t^4\), we will follow these steps:

### Step 1: Differentiate \(x\) with respect to \(t\)
We start by differentiating \(x\) with respect to \(t\):
\[ \frac{dx}{dt} = \frac{d}{dt}(2a t^2) = 2a \cdot 2t = 4a t \]

...