# 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, $$q + at^2$$).