A(-2,3),B(-2,5) and C (4,-1)
Since all the points will be equidistant from (h,k). Because we have the same x values for two of the points, we can solve this equation for k..... [ we are actually setting r^2 = r^2 ]
(h + 2)^2 + (k - 3)^2 = ( h + 2)^2 + ( k - 5)^2 subtract the first terms of each side out and we have that
(k -3)^2 = (k - 5)^2 expand
k^2 - 6k + 9 = k^2 - 10k + 25 subtract k^2 from both sides
-6k + 9 = -10k + 25 add 10k to both sides, subtract 9 from both sides
4k = 16 divide both sides by 4
k = 4
Now...we can find h thusly using the distance formula
( h + 2)^2 + (4 -3)^2 = (h -4)^2 + (4 + 1)^2 simplify
h^2 + 4h + 4 + 1 = h^2 - 8h + 16 + 25
12h = 36
h = 3
So the center is ( 3, 4)
And the radius can be found thusly
(3 + 2)^2 + 1^2 = r^2
26 = r^2
√26 = r
And the equation is
(x - 3)^2 + (y - 4)^2 = 26
Here's the graph with the center and points shown : https://www.desmos.com/calculator/othhfgdve0
