Question

The center of a circle is (h, 5) and the radius is 10. The circle passes through (2, –3). Find the two possible values of h.

Answer 1

Check out the photo I attached. You first start with the basic equation of a circle:
(x - h)² + (y - k)² = r²
Where (h, k) is the vertex and r is the radius. We are told that the vertex is (h, 5) and the radius is 10, so substitute those values in to get:
(x - h)² + (y - 5)² = 100
Now, to find h, substitute the point given, (2, -3), for the variables x and y:
(2 - h)² + (-3 - 5)² = 100
Finally, simplify then solve for h by factoring algebraically. Your answers should be h = 4 and h = 8.