00:01
Okay, so we have an ellipse in a rotated frame.
00:04
I just want to point out that for this ellipse as drawn, the center of the ellipse is at the origin in both the xy plane and in the x prime y prime plane.
00:15
So one thing we see right away is that x prime zero, that's equal to y prime zero, and that's zero.
00:28
Okay.
00:30
So our main interest is figuring out how to rotate the coordinates here.
00:36
All right.
00:37
So here's what we know.
00:40
Okay.
00:42
And then let's substitute these in.
00:45
And then we're going to put this into standard form.
00:48
So the standard form they have written down here, there is always some ambiguity in it, but they tell us what f is supposed to look like.
00:58
But here's the thing that's really interesting.
01:01
Any quadratic curves that include circles, ellipses, parabolas, hyperbolas, and even straight lines can be defined by this equation, depending on what values we choose for a, b, c, d, e, and f.
01:27
So we want to find out what they are in particular for this situation...