00:01
In this question, we want to find a vector function that represents the curve of intersection of the two surfaces.
00:08
Here we have the paraboloid z equals 4x squared plus y squared and the parabolic cylinder y equals x squared.
00:19
So we're going to deal with the easier one first.
00:22
We're going to start with y equals x squared.
00:25
And we're going to have to introduce a parameter t.
00:30
So specifically, i am going to let x equal t.
00:35
If x is equal to t, then y, since that was equal to x squared, my y is equal to t squared.
00:45
Now, i need to figure out what z is in terms of t as well.
00:50
But remember, z was equal to 4x squared plus y squared.
00:56
So we're going to do a substitution.
00:58
I'm going to replace my x with t and my y with t squared...