If `x=2at` at `y=a t^2` , where `a` is a constant, then `(d^2y)/(dx^2)` at `x=1/2` is `(a)1//2a` (b) 1 (c) `2a` (d) none of these

Explanation

`x=2 a t, y=a t^{2}`
`
frac{d x}{d t}=2 a ; frac{d y}{d t}=2 a t`
`
frac{d y}{d x}=frac{frac{d y}{d t}}{frac{d x}{d t}}=t`
`
frac{d^{2} y}{d x^{2}}=frac{frac{d}{d t}(frac{d y}{d x})}{frac{d x}{d t}}=frac{1}{2 a}`
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