The first thing we must do for this case is to use the formula of the midpoint to find the center of the circle.
We have then:
[tex]C = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2})
[/tex]
Substituting values we have:
[tex]C = ( \frac{-6 + 2}{2} , \frac{-8 + 10}{2}) [/tex]
[tex]C = ( \frac{-4}{2} , \frac{2}{2}) [/tex]
[tex]C = (-2, 1)[/tex]
We are now looking for the radius of the circle. For this, we use the formula of distance between points.
We have then:
[tex]r = \sqrt{(x2-x1)^2 + (y2-y1)^2} [/tex]
Substituting values we have:
[tex]r = \sqrt{(2-(-2))^2 + (10-1)^2} [/tex]
[tex]r = \sqrt{(4)^2 + (9)^2} [/tex]
[tex]r = \sqrt{16 + 81} [/tex]
[tex]r = \sqrt{97} [/tex]
We now write the standard equation of the circle:
[tex](x-xo)^2 + (y-yo)^2 = r^2[/tex]
Substituting values we have:
[tex](x+2)^2 + (y-1)^2 = 97[/tex]
