The center of a circle is (h, 7) and the radius is 10. The circle passes through (3, -1). Find all possible values of h.

Answer 1

(h,7) must lie on a circle of radius 10 , centered at (3,-1)

(x - 3)^2 + (y + 1)^2 = 10^2

(h - 3)^2 + (7 + 1)^2 = 10^2 ... (h - 3)^2 = 100 - 64 = 36

h - 3 = ±6

Answer 2

Scott used the wrong point for the center.

I see it as:

(x-h)^2 + (y-7)^2 = 100
now plug in (3,-1)
(3-h)^2 + (-1-7)^2 = 100
(3-h)^2 = 100 - 64
3-h = ±6
h = 3 ±6

Bonus question: Why did Scott get the same result, even though he had the
incorrect center ?