Match the following with the parametric equation of the parabola:

x = a t^{2}, y = 2 a t

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x = - a t^{2}, y = 2 a t

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x = 2 a t, y = a t^{2}

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x = 2 a t, y = - a t^{2}

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Solution

The requirements of a parametric representation are it should be able to represent every point on the curve and it should also satisfy the equation of the curve.

But we usually take $(a t^{2}, 2 a t)$ for $y^{2} = 4 a x .$ In our question, we will just substitute and check if it satisfy any equation.

But we need to remember these parametric representation as it will be used later. After substituting and checking, we get,

$y^{2} = 4 a x \to x = a t^{2}, y = 2 a t$

$x^{2} = 4 a y \to x = 2 a t, y = a t^{2}$

$y^{2} = - 4 a x \to x = - a t^{2}, y = 2 a t$

$x^{2} = - 4 a y \to x = 2 a t, y = - a t^{2}$

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Similar questions

Which of the following points lie on the parabola $x^{2} = 4 a y ?$

\frac{d^{2} y}{d x^{2}}

x = a t^{2}, y = 2 a t

x = a t^{2}, y = 2 a t

\frac{d^{2} y}{d x^{2}} =

x = a t^{2}, y = 2 a t

\frac{d^{2} x}{d y^{2}} =

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