00:01
In this problem, we're practicing finding the traces for given equations and values.
00:06
So for a, we have 4x squared plus y squared plus z squared is equal to 4.
00:15
We want to find the trace at y equal to 1.
00:19
And so in each of these, we want to determine whether the equation of the trace is an ellipse, parabola, or hyperbola.
00:25
So we have 4x squared plus 1 plus z squared is equal to 4.
00:30
So then we're going to have 4x squared plus z squared is equal to 3.
00:37
So this is going to be an ellipse.
00:41
And we can even write it as 4 thirds x squared plus z squared over 3 is equal to 1 if you wanted to.
00:50
Next we have 4x squared plus y squared plus z squared is equal to 4.
00:57
It's the same equation, but we're looking at the trace for x equals 1 half.
01:03
So it's going to be one half squared is one fourth.
01:06
So we're going to get one plus y squared plus z squared is equal to four...