Calc 2: Curves Defined by parametric equations

[MillerGenuine]

these are fairly simple questions that only require you to plot points and then find a Cartesian equation of the curve. My question is when trying to solve for the Cartesian Equation, whether to solve for X first or Y? I will give an example.

X=3t-5 , y=2t + 1
Graphing this is simple, solving for Cartesian equation of the curve by eliminating the parameter is fairly simple,

x=3t-5 therefore t=(x+5)/3

Subsitute t into y=2t+1 and you get y=2/3(x+5) + 1

easy enough.

Now in the following problem

x=(t^2)-2 , y=5-2t

again, graphing is simple, but this time to find the Cartesian equation they first solve for t like so..

y=5-2t therefore t=(y-5)/2

then x= 1/4 (y-5)^2 - 2

So does it matter whether I have my Cartesian equation in the Form of X=... or Y=...
or do i just take the easiest path to solve for "t" and substitute?

 

[tiny-tim]

Hi MillerGenuine!

So does it matter whether I have my https://www.physicsforums.com/library.php?do=view_item&itemid=229" equation in the Form of X=... or Y=...
or do i just take the easiest path to solve for "t" and substitute?

It doesn't matter …

follow the path of least effort! :zzz:​