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, \(q + at^2\)).
