00:02
For this problem, i'm going to start by sketching each circle.
00:06
And if you can do it with a compass and a straight edge that is even better for accuracy.
00:12
I'm just going to have a rough sketch.
00:14
So my first circle is going to have center to one and radius five.
00:20
So we can sketch that.
00:22
From the center, i'll go up five and right five and down five and left five.
00:30
So here's our circle.
00:36
And then for the second one, it's going to have center negative 2, 2, and radius 4.
00:41
So let's go ahead and sketch that.
00:54
And for the third one, it's going to have center 1, negative 2, and radius 3.
00:59
So we'll sketch that.
01:08
Okay.
01:09
So we're looking for the point of intersection of these three circles, because that would be the epicenter of the earthquake.
01:18
And it's looking like it would be around here somewhere.
01:20
Let's go ahead and algebraically find that point.
01:25
So what i'm going to do is take these equations and translate them into something closer to general form.
01:32
So i'm going to multiply things out.
01:34
For the first equation we would get x squared minus 4x plus 4 plus y squared minus 2y plus 1 equals 25.
01:47
And combining the constants together we get x squared minus 2y plus 1.
01:51
4x plus y squared minus 2y equals 20.
01:57
For the second equation, multiplying it out, we have x squared plus 4x plus 4 plus y squared minus 4y plus 4 equals 16...