[tex]\text{centre = (}\frac{1}{2}\text{ (-4 + 4), }\frac{1}{2}(1-5))\text{ = (}0,-2)\text{ }[/tex]
the radius is the distance from the centre to either of the 2 given points
Let (x1, y1) = (-4,1) and (x2,y2) = (4,-5) (the given points)
then:
[tex]r\text{ = d = }\sqrt[]{(4-(-4))^2+(-5-1)^2}\text{ = }\sqrt[]{(8)^2+(-6)^2\text{ = }}\text{ 10}[/tex]
then, take the equation of the circle is:
[tex](x-0)^2+(y+2)^2\text{ = 10}[/tex]
that is:
[tex](x)^2+(y+2)^2\text{ = 10}[/tex]
