00:01
So for this problem, we've been given this rectangular equation, and we want to find some parameterizations for it.
00:08
To begin, we note that the domain of x is from minus infinity to infinity, because no matter what number we pick, we can cube it.
00:18
So x domain is the full real numbers.
00:24
So let's pick our first parameterization as a simple one, and just set x equal to t.
00:31
With this, we can simply make the substitution into the original equation, and we see that y becomes t cubed, and this gives us a parameterization of the original curve.
00:45
The only thing that remains to be done is to get the domain of t, but as we've simply changed the name of x, if you will, the domain of t is simply the domain of x.
00:58
So this is our first parameterization.
01:01
Now for the second one, we're going to, instead of setting x equal to t, we're going to set y equal to t...