Which of the following can be the parametric equation of $x^{2} = 4 a y$

$(a t^{2}, 2 a t)$

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$(2 a t, a t^{2})$

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$(- 2 a t, a t^{2})$

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$(a t^{2}, - 2 a t)$

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Solution

The correct option is C
$(- 2 a t, a t^{2})$

There can be more than one parametric representation of a given parabola. One condition is that it should be able to represent all points and should satisfy the curves equation.

So by substituting the given options, we get $B$ and $C$ as correct. That is $(2 a t, a t^{2})$ and $(- 2 a t, a t^{2})$ are parametric representations of $x^{2} = 4 a y$

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