00:01
So in this question, we're asked to sketch the contour plot of f of xy equals 4x squared plus y squared using level curves of height k equals 0, 4, and 16.
00:13
So what does that mean? if i'm going to have the level curve of height 0, that means i am going to set f xy equal to 0.
00:24
So 4x squared plus y squared equals 0.
00:29
Where does that happen? well, notice, both of these guys are perfect squares, which means they are each positive.
00:40
4x squared is, well, at least non -negative, greater than or equal to zero, while y -squared is also greater than or equal to zero.
00:50
And so the sum here is always greater than equal to zero.
00:54
The only time that 4x squared plus y squared could possibly be equal to 0 is if you were at the origin, if x and y were both equal to 0.
01:08
So the level curve corresponding to k equals 0 is actually just the origin.
01:18
It's not even a curve, it's just a point.
01:21
Then what about the level curve of height k equals 4? now i'm setting 4x squared plus y squared equal to 4.
01:34
What shape is that? if i were to graph this, this is an ellipse.
01:41
This is an ellipse.
01:42
What are the intercepts of it? well, my x intercepts, they're found by setting y equal to zero.
01:52
You have 4x squared equals 4, x squared equals 1, x equals plus or minus 1...