The equation for the midpoint is given by:
[tex]P = (\frac{x1 + x2}{2} , \frac{y1 + y2}{2}) [/tex]
Substituting values we have:
[tex]P = (\frac{-10 + 4}{2} , \frac{-2 + 6}{2}) [/tex]
[tex]P = (\frac{-6}{2} , \frac{4}{2}) [/tex]
[tex]P = (-3 , 2) [/tex]
We can find the radius of the circle using the equation of distance between points:
[tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2} [/tex]
Substituting values:
[tex]d = \sqrt{(4-(-3))^2 + (6-2)^2} [/tex]
[tex]d = \sqrt{(4+3)^2 + (4)^2} [/tex]
[tex]d = \sqrt{(7)^2 + (4)^2} [/tex]
[tex]d = \sqrt{49 + 16} [/tex]
[tex]d = \sqrt{65} [/tex]
The equation of the circle is its standard form is:
[tex](x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2
[/tex]
Where,
(xo, yo): coordinates of the center of the circle
r: radius of the circle
Substituting values:
[tex](x + 3) ^ 2 + (y-2) ^ 2 = 65
[/tex]
