00:01
All right, so we have some circle, and it's going through the points, negative 2, 7.
00:06
So i'll draw, like, this is going to be a horrible -looking sketch, but oh, well.
00:11
Negative 2, 7 is here.
00:13
Zero, 1 is, like, right here.
00:16
And then 2, oh, boy.
00:22
Hmm.
00:27
2, negative 1 is here.
00:31
Okay, so our circle, let's see if i can draw.
00:35
It's going to, like this is, like our circle is going to like, it's barely curved.
00:40
And our circle is going to look something like that, but whatever.
00:44
Okay.
00:45
Now, here's what we got.
00:46
We have a little chord between these two points.
00:50
And we have a little chord between these two points.
00:54
Okay.
00:55
So, 2 comma negative 1 is this one.
01:05
0 comma 1 is this one here.
01:10
And negative 2 comma 7 is this one up here.
01:14
So if we want to find the radius in the center, if we want to find this radius in the center, so first i'm going to find the equations of all these lines.
01:23
So that purple line, it's going to be y minus 1 equals the slope times x, and i got to find the slope between those two points.
01:33
Well, from 7 to 1, i go down 6, and i go to the right two.
01:40
So negative six over two is negative three.
01:44
So y equals negative three x plus one is the slope or is the equation of that purple line.
01:52
I'm going to do the same thing for the red line.
01:55
Y minus one equals some slope and then it's going to be x minus zero again.
02:01
And i got to find the slope of this red line.
02:04
Well, i have to go down two and over two.
02:07
So my slope here is negative one.
02:10
So y equals, okay, i guess i didn't have to do all of this, but so y is going to equal negative x plus one.
02:24
When i solve it, they're going to hit at zero comma one.
02:27
Anyway, here's what we want to do now.
02:30
So for this red chord right here, i got to figure out what's right in the middle.
02:36
I got to find the perpendicular bisector of this red cord and i'm gonna got to find the equation of this line right here so because the slope of the red cord is negative one that dotted line is going to have a slope of positive one because they're negative reciprocals of each other so so the equation of that dotted line, which is going to be a diameter of the circle, that's going to be y minus something equals 1 times x minus something.
03:20
This point right here is the midpoint between 0, 1 and 2, negative 1, which is the point.
03:29
It looks like it's going to be 1, 0.
03:40
1, 0...
