If $x = t^{2} + 2$ and $y = 2 t$ represent the parametric equation of the parabola

x^{2} = 4 (y - 2)

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(y - 2)^{2} = 4 x

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y^{2} = 4 (x - 2)

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(x - 2)^{2} = 4 y

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Solution

The correct option is B $y^{2} = 4 (x - 2)$
We have, $x = t^{2} + 2$ ..........(1)
and $y = 2 t \Rightarrow t = \frac{y}{2}$ .........(2)
From second equation substitute value of $y$ in terms of $t$ in (1)
$\Rightarrow x = \frac{y^{2}}{4} + 2$

$\Rightarrow \frac{y^{2}}{4} = x - 2$

$\Rightarrow y^{2} = 4 (x - 2)$

Hence option 'C' is correct choice

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