Answer:
[tex](x - 8)^{2} + (y - 14)^{2} = 100[/tex]
Step-by-step explanation:
The equation of a circle has the following format:
[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]
In which r is the radius(half the diameter) and the centre is the point [tex](x_{0}, y_{0})[/tex]
Points F(2,6) and G(14,22) are the endpoints of a diameter of circle M.
To find the diameter, we find the distance between these two points. So
[tex]D = \sqrt{(14 - 2)^{2} + (22 - 6)^{2}} = \sqrt{12^{2} + 16^{2}} = 20[/tex]
So
[tex]r = \frac{D}{2} = 10[/tex]
The centre is the midpoint between F and G. So
[tex]x_{0} = \frac{2 + 14}{2} = 8[/tex]
[tex]y_{0} = \frac{6 + 22}{2} = 14[/tex]
The equation is:
[tex](x - 8)^{2} + (y - 14)^{2} = 100[/tex]
