The difference between cartesian and parametric equations? (1 Viewer)

[FDownes]

I have to admit I've never really understood the difference between a cartesian and a parametric equation.

From what I can gather, the difference is that a cartesian equation involves both the x and the y coordinates in the same equation (e.g. y = x²) while a parametric equation uses another variable as a 'go between' for the two equations (e.g. y = t² and x = t).

Could someone please help clear this up with a simple explanation? I find it almost impossible to find the cartesian equation when asked, so I could really use some help.

Also, if anyone could offer any tips for finding the parametric equation they'd be greatly appreciated.

 

[henry08]

You are exactly correct in what you said.

 

[gurmies]

Yep, you are correct in what you said. It's simply linking two variables through the medium of a third. Now you say you have trouble finding cartesian equations. This is actually very simple, observe:

Suppose x = 2at (1) and y = at^2 (2)

Therefore, making "t" the subject in (1), t = x/2a. Now we can substitute this into (2):

y = a (x/2a)^2
y= a(x^2/4a^2)
y= x^2/4a
x^2 = 4ay

Which is the general parabola expressed in terms of it's vertex and focal length "a".