This circle passes through the points (-1, 2), (3,2) and (9,0). The center of the circle is at (h,k). What is the value of h+k?
+128475 The form is (x - h)^2 + (y - k)^2 = r^2
Using the first two points and the square of the distance formula to equate the radius's we have
(-1-h)^2 + ( 2 - k)^2 = (3-h)^2 + (2 - k)^2
h^2 + 2h + 1 = h^2 - 6h + 9
8h = 8
h = 1 this is the x coordinate of the center
Using the last two points and doing the same thing we have
(3 - 1)^2 + (2 - k)^2 = (9 - 1)^2 + (0 - k)^2
4 + k^2 -4k + 4 = 64 + k^2
-4k + 8 = 64
-4k = 56
k= -14
h + k = 1 - 14 = -13
