MillerGenuine
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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?
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?
