00:01
This problem, what we're being asked to do is write the equation for a circle when we're given the endpoints for the diameter.
00:05
Well, what's our general equation for a circle? it looks like this.
00:09
Is x minus h squared plus y minus k squared equals r squared, where hk is the ordered pair for our center, and r is the radius.
00:22
So once we have the center and the radius, we can write our equation.
00:25
Well, because we're given the endpoints of the diameter, remember the center is directly in between.
00:29
So to find our center, what we're going to do is we're going to find the midpoint between those two points.
00:35
So i'm going to call this point m.
00:37
Well, to find the midpoint, what we do is we take the average of the x values.
00:40
So at x of 1 plus x of 2 divided by 2, that will be its x coordinate.
00:44
Then for the y coordinate, we find the average between the two y values.
00:48
So now we can go ahead and find our midpoint.
00:51
So for our x values, we have negative 2 and 6.
00:54
So we're going to have negative 2 plus 6 getting divided by 2.
00:57
And for our y values, we have 1 and negative 5.
00:59
So we're going to have 1 plus negative 5 divided by 2.
01:03
Well, negative 2 plus 6 is 4 and 4 divided by 2 is 2.
01:07
So that will be the x coordinate.
01:09
And for our y values, 1 plus negative 5 is negative 4 and negative 4 divided by 2 is negative 2.
01:15
So now we have our midpoint, which represents the center for our circle...