The equation for a circle is:
[tex](x-a)^{2} + (y-b)^{2} + = r^{2}[/tex]
Where (a,b) is the circle's center and r is the circle's radius.
First, we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.
The formula to find the mid-point of a line segment giving the two endpoints is:
M = [tex](\frac{x_{1} + x_{2} }{2}[/tex], [tex]\frac{y_{1} + y_{2} }{y} )[/tex]
Where M is the midpoint and the given points are:
[tex](x_{1}, y_{1} )[/tex] and [tex](x_{2} , y_{2})[/tex]
Substituting the values from the two points in the problem gives:
[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{-2+4}{2} )[/tex]
[tex]M = (\frac{11+9}{2}[/tex],[tex]\frac{2-4}{2})[/tex]
[tex]M = (\frac{20}{2} , \frac{2}{2})[/tex]
[tex]M = (10,1)[/tex]
