Thanks, geno....here's another option for the first one......since the distance from the center to all points is the same....set the radiuses equal....so, using the first and third point, we have
(-2 - h)^2 + (2- k)^2 = (6 - h)^2 + (2-k)^2 subtract (2-k)^2 from both sides
(h + 2)^2 = (h - 6)^2 expand
h^2 + 4h + 4 = h^2 -12h + 36 subtract h^2 from both sides
4h + 4 = -12h + 36 add 12h to both sides........subtract 4 from each side
16h = 32 divide both sides by 16
h = 2 this is the x coordinate of the center
Since the point (2, -2) is on the graph and the x coordinate of the center is 2.......the radius must be [2 - (-2)] = 4
And using (2, -2)....we can find the y coordinate of the center = k, thusly
(2 - 2)^2 + (-2 - k)^2 = 16
k^2 + 4k + 4 = 16
k^2 + 4k - 12 = 0
(k -2)(k + 6) = 0 so = -6 or k = 2 but k can't = - 6 since the lowest y coordinate on the graph is -2.....so k = 2
Ad the equation of the circle is
(x - 2)^2 + (y - 2)^2 = 4^2
(x - 2)^2 + ( y - 2)^2 = 16
Here's the graph : https://www.desmos.com/calculator/bggiezt02g
