00:01
Problem 41 asks us to find the standard form equation for the circle with the endpoints of a diameter of 1 ,4, and negative 3, comma, 2.
00:14
So, we'll first recall the standard form equation, x minus h squared plus y minus k squared equals r squared.
00:23
Now, in order to write the standard form equation for our circle, we'll have to solve for h, k, and r.
00:29
So first to find the center point h comma k or midpoint of the line of our circle, we can simply plug in the values for x1, x2, y1, and y2.
00:47
So given these two points, one is x1, 4 is y1, negative 3 is x2, and 2 is y2.
00:59
So we can solve for our center point, h comma k.
01:13
For h, we have 1 plus negative 3 over 2, comma, 4 plus 2 over 2.
01:43
So we get 1 plus negative 3 or 1 minus 3, negative 2, divided by 2, comma, 4 plus 2, 6, x divided by 2.
01:58
So our center, h comma k, equals negative 1, comma, 3.
02:10
So now that we know negative 1 and 3, we can plug them into our standard form equation.
02:21
So our standard form will look like this, x minus h or x minus negative 1 squared plus y minus 3 squared equals r, so now we have to solve for r.
02:44
And we remember the distance equation...