Parametric Equation of all Forms of Parabola

Here you will learn what is the parametric equation of all forms of parabola and their parametric coordinates.

Let’s begin –

Parametric Equation of Parabola and Coordinates

(i) For the parabola \(y^2\) = 4ax :

The parametric equation is x = \(at^2\) & y = 2at.

And parametric coordinates are (\(at^2\), 2at).

(ii) For the parabola \(y^2\) = -4ax :

The parametric equation is x = \(-at^2\) & y = 2at.

And parametric coordinates are (\(-at^2\), 2at).

(iii) For the parabola \(x^2\) = 4ay :

The parametric equation is x = 2at & y = \(at^2\).

And parametric coordinates are (2at, \(at^2\)).

Also Read : Different Types of Parabola Equations

(iv) For the parabola \(x^2\) = -4ay :

The parametric equation is x = 2at & y = \(-at^2\).

And parametric coordinates are (2at, -\(at^2\)).

(v) For the parabola \((y – k)^2\) = 4a(x – h) :

The parametric equation is x = \(h + at^2\) & y = k + 2at.

And parametric coordinates are (\(h + at^2\), k + 2at).

(vi) For the parabola \((x – p)^2\) = 4a(y – q) :

The parametric equation is x = p + 2at & y = \(q + at^2\).

And parametric coordinates are (p + 2at, \(q + at^2\)).

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