Convention in parametric equation of parabola.

[vkash]

general equation of parabola is y^2=4*a*x. it's parametric equation is ((a*t^2),(2*a*t)) [as in my book] but i think there can be other kind of parametric equations also like( ((t^2)/4*a),t) it defines a parabola easily. is using ((a*t^2),(2*a*t)) as parametric equation of parabola is convention or there is any reason for this.
I think it's a convention but some question are specially based on this equation ((a*t^2),(2*a*t)) so i want to confirm is it really a convention or there is any other thing.

thanks for reading. write your view.

 

[micromass]

Hi vkash!

There aren't really any good reasons for taking (at²,2at) as parametrization. The only good reason that I can think of is that we don't work with fractions with this parametrization, and fractions are sometimes annoying.

 

[vkash]

Hi vkash!

There aren't really any good reasons for taking (at²,2at) as parametrization. The only good reason that I can think of is that we don't work with fractions with this parametrization, and fractions are sometimes annoying.

thanks genius.